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        <a href="spade-module.html">Package&nbsp;spade</a> ::
        Module&nbsp;logic
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<h1 class="epydoc">Source Code for <a href="spade.logic-module.html">Module spade.logic</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">   1</tt>  <tt class="py-line"><tt class="py-docstring">"""Representations and Inference for Logic (Chapters 7-10)</tt> </tt>
<a name="L2"></a><tt class="py-lineno">   2</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L3"></a><tt class="py-lineno">   3</tt>  <tt class="py-line"><tt class="py-docstring">Covers both Propositional and First-Order Logic. First we have four</tt> </tt>
<a name="L4"></a><tt class="py-lineno">   4</tt>  <tt class="py-line"><tt class="py-docstring">important data types:</tt> </tt>
<a name="L5"></a><tt class="py-lineno">   5</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L6"></a><tt class="py-lineno">   6</tt>  <tt class="py-line"><tt class="py-docstring">    KB            Abstract class holds a knowledge base of logical expressions</tt> </tt>
<a name="L7"></a><tt class="py-lineno">   7</tt>  <tt class="py-line"><tt class="py-docstring">    KB_Agent      Abstract class subclasses agents.Agent</tt> </tt>
<a name="L8"></a><tt class="py-lineno">   8</tt>  <tt class="py-line"><tt class="py-docstring">    Expr          A logical expression</tt> </tt>
<a name="L9"></a><tt class="py-lineno">   9</tt>  <tt class="py-line"><tt class="py-docstring">    substitution  Implemented as a dictionary of var:value pairs, {x:1, y:x}</tt> </tt>
<a name="L10"></a><tt class="py-lineno">  10</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L11"></a><tt class="py-lineno">  11</tt>  <tt class="py-line"><tt class="py-docstring">Be careful: some functions take an Expr as argument, and some take a KB.</tt> </tt>
<a name="L12"></a><tt class="py-lineno">  12</tt>  <tt class="py-line"><tt class="py-docstring">Then we implement various functions for doing logical inference:</tt> </tt>
<a name="L13"></a><tt class="py-lineno">  13</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L14"></a><tt class="py-lineno">  14</tt>  <tt class="py-line"><tt class="py-docstring">    pl_true          Evaluate a propositional logical sentence in a model</tt> </tt>
<a name="L15"></a><tt class="py-lineno">  15</tt>  <tt class="py-line"><tt class="py-docstring">    tt_entails       Say if a statement is entailed by a KB</tt> </tt>
<a name="L16"></a><tt class="py-lineno">  16</tt>  <tt class="py-line"><tt class="py-docstring">    pl_resolution    Do resolution on propositional sentences</tt> </tt>
<a name="L17"></a><tt class="py-lineno">  17</tt>  <tt class="py-line"><tt class="py-docstring">    dpll_satisfiable See if a propositional sentence is satisfiable</tt> </tt>
<a name="L18"></a><tt class="py-lineno">  18</tt>  <tt class="py-line"><tt class="py-docstring">    WalkSAT          (not yet implemented)</tt> </tt>
<a name="L19"></a><tt class="py-lineno">  19</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L20"></a><tt class="py-lineno">  20</tt>  <tt class="py-line"><tt class="py-docstring">And a few other functions:</tt> </tt>
<a name="L21"></a><tt class="py-lineno">  21</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L22"></a><tt class="py-lineno">  22</tt>  <tt class="py-line"><tt class="py-docstring">    to_cnf           Convert to conjunctive normal form</tt> </tt>
<a name="L23"></a><tt class="py-lineno">  23</tt>  <tt class="py-line"><tt class="py-docstring">    unify            Do unification of two FOL sentences</tt> </tt>
<a name="L24"></a><tt class="py-lineno">  24</tt>  <tt class="py-line"><tt class="py-docstring">    diff, simp       Symbolic differentiation and simplification             </tt> </tt>
<a name="L25"></a><tt class="py-lineno">  25</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L26"></a><tt class="py-lineno">  26</tt>  <tt class="py-line"> </tt>
<a name="L27"></a><tt class="py-lineno">  27</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">__future__</tt> <tt class="py-keyword">import</tt> <tt class="py-name">generators</tt> </tt>
<a name="L28"></a><tt class="py-lineno">  28</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">re</tt> </tt>
<a name="L29"></a><tt class="py-lineno">  29</tt>  <tt class="py-line"><tt class="py-comment">#import agents</tt> </tt>
<a name="L30"></a><tt class="py-lineno">  30</tt>  <tt class="py-line"><tt class="py-comment">#from utils import *</tt> </tt>
<a name="L31"></a><tt class="py-lineno">  31</tt>  <tt class="py-line"> </tt>
<a name="every"></a><div id="every-def"><a name="L32"></a><tt class="py-lineno">  32</tt> <a class="py-toggle" href="#" id="every-toggle" onclick="return toggle('every');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#every">every</a><tt class="py-op">(</tt><tt class="py-param">predicate</tt><tt class="py-op">,</tt> <tt class="py-param">seq</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="every-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="every-expanded"><a name="L33"></a><tt class="py-lineno">  33</tt>  <tt class="py-line">    <tt class="py-docstring">"""True if every element of seq satisfies predicate.</tt> </tt>
<a name="L34"></a><tt class="py-lineno">  34</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; every(callable, [min, max])</tt> </tt>
<a name="L35"></a><tt class="py-lineno">  35</tt>  <tt class="py-line"><tt class="py-docstring">    1</tt> </tt>
<a name="L36"></a><tt class="py-lineno">  36</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; every(callable, [min, 3])</tt> </tt>
<a name="L37"></a><tt class="py-lineno">  37</tt>  <tt class="py-line"><tt class="py-docstring">    0</tt> </tt>
<a name="L38"></a><tt class="py-lineno">  38</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L39"></a><tt class="py-lineno">  39</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt id="link-0" class="py-name" targets="Variable spade.bdi.x=spade.bdi-module.html#x,Variable spade.logic.x=spade.logic-module.html#x"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-0', 'x', 'link-0');">x</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">seq</tt><tt class="py-op">:</tt> </tt>
<a name="L40"></a><tt class="py-lineno">  40</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">predicate</tt><tt class="py-op">(</tt><tt id="link-1" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-1', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
<a name="L41"></a><tt class="py-lineno">  41</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
</div><a name="L42"></a><tt class="py-lineno">  42</tt>  <tt class="py-line"> </tt>
<a name="isnumber"></a><div id="isnumber-def"><a name="L43"></a><tt class="py-lineno">  43</tt> <a class="py-toggle" href="#" id="isnumber-toggle" onclick="return toggle('isnumber');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#isnumber">isnumber</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="isnumber-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="isnumber-expanded"><a name="L44"></a><tt class="py-lineno">  44</tt>  <tt class="py-line">    <tt class="py-docstring">"Is x a number? We say it is if it has a __int__ method."</tt> </tt>
<a name="L45"></a><tt class="py-lineno">  45</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">hasattr</tt><tt class="py-op">(</tt><tt id="link-2" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-2', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-string">'__int__'</tt><tt class="py-op">)</tt> </tt>
</div><a name="L46"></a><tt class="py-lineno">  46</tt>  <tt class="py-line"> </tt>
<a name="issequence"></a><div id="issequence-def"><a name="L47"></a><tt class="py-lineno">  47</tt> <a class="py-toggle" href="#" id="issequence-toggle" onclick="return toggle('issequence');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#issequence">issequence</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="issequence-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="issequence-expanded"><a name="L48"></a><tt class="py-lineno">  48</tt>  <tt class="py-line">    <tt class="py-docstring">"Is x a sequence? We say it is if it has a __getitem__ method."</tt> </tt>
<a name="L49"></a><tt class="py-lineno">  49</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">hasattr</tt><tt class="py-op">(</tt><tt id="link-3" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-3', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-string">'__getitem__'</tt><tt class="py-op">)</tt> </tt>
</div><a name="L50"></a><tt class="py-lineno">  50</tt>  <tt class="py-line"> </tt>
<a name="num_or_str"></a><div id="num_or_str-def"><a name="L51"></a><tt class="py-lineno">  51</tt> <a class="py-toggle" href="#" id="num_or_str-toggle" onclick="return toggle('num_or_str');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#num_or_str">num_or_str</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="num_or_str-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="num_or_str-expanded"><a name="L52"></a><tt class="py-lineno">  52</tt>  <tt class="py-line">    <tt class="py-docstring">"""The argument is a string; convert to a number if possible, or strip it.</tt> </tt>
<a name="L53"></a><tt class="py-lineno">  53</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; num_or_str('42')</tt> </tt>
<a name="L54"></a><tt class="py-lineno">  54</tt>  <tt class="py-line"><tt class="py-docstring">    42</tt> </tt>
<a name="L55"></a><tt class="py-lineno">  55</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; num_or_str(' 42x ')</tt> </tt>
<a name="L56"></a><tt class="py-lineno">  56</tt>  <tt class="py-line"><tt class="py-docstring">    '42x'</tt> </tt>
<a name="L57"></a><tt class="py-lineno">  57</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L58"></a><tt class="py-lineno">  58</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-4" class="py-name" targets="Function spade.logic.isnumber()=spade.logic-module.html#isnumber"><a title="spade.logic.isnumber" class="py-name" href="#" onclick="return doclink('link-4', 'isnumber', 'link-4');">isnumber</a></tt><tt class="py-op">(</tt><tt id="link-5" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-5', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-6" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-6', 'x', 'link-0');">x</a></tt> </tt>
<a name="L59"></a><tt class="py-lineno">  59</tt>  <tt class="py-line">    <tt class="py-keyword">try</tt><tt class="py-op">:</tt> </tt>
<a name="L60"></a><tt class="py-lineno">  60</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">int</tt><tt class="py-op">(</tt><tt id="link-7" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-7', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt>  </tt>
<a name="L61"></a><tt class="py-lineno">  61</tt>  <tt class="py-line">    <tt class="py-keyword">except</tt> <tt class="py-name">ValueError</tt><tt class="py-op">:</tt> </tt>
<a name="L62"></a><tt class="py-lineno">  62</tt>  <tt class="py-line">        <tt class="py-keyword">try</tt><tt class="py-op">:</tt> </tt>
<a name="L63"></a><tt class="py-lineno">  63</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">float</tt><tt class="py-op">(</tt><tt id="link-8" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-8', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt>  </tt>
<a name="L64"></a><tt class="py-lineno">  64</tt>  <tt class="py-line">        <tt class="py-keyword">except</tt> <tt class="py-name">ValueError</tt><tt class="py-op">:</tt> </tt>
<a name="L65"></a><tt class="py-lineno">  65</tt>  <tt class="py-line">                <tt class="py-keyword">return</tt> <tt class="py-name">str</tt><tt class="py-op">(</tt><tt id="link-9" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-9', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">strip</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L66"></a><tt class="py-lineno">  66</tt>  <tt class="py-line"> </tt>
<a name="L67"></a><tt class="py-lineno">  67</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L68"></a><tt class="py-lineno">  68</tt>  <tt class="py-line"> </tt>
<a name="KB"></a><div id="KB-def"><a name="L69"></a><tt class="py-lineno">  69</tt> <a class="py-toggle" href="#" id="KB-toggle" onclick="return toggle('KB');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="spade.logic.KB-class.html">KB</a><tt class="py-op">:</tt> </tt>
</div><div id="KB-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="KB-expanded"><a name="L70"></a><tt class="py-lineno">  70</tt>  <tt class="py-line">    <tt class="py-docstring">"""A Knowledge base to which you can tell and ask sentences.</tt> </tt>
<a name="L71"></a><tt class="py-lineno">  71</tt>  <tt class="py-line"><tt class="py-docstring">    To create a KB, first subclass this class and implement</tt> </tt>
<a name="L72"></a><tt class="py-lineno">  72</tt>  <tt class="py-line"><tt class="py-docstring">    tell, ask_generator, and retract.  Why ask_generator instead of ask?  </tt> </tt>
<a name="L73"></a><tt class="py-lineno">  73</tt>  <tt class="py-line"><tt class="py-docstring">    The book is a bit vague on what ask means --</tt> </tt>
<a name="L74"></a><tt class="py-lineno">  74</tt>  <tt class="py-line"><tt class="py-docstring">    For a Propositional Logic KB, ask(P &amp; Q) returns True or False, but for an</tt> </tt>
<a name="L75"></a><tt class="py-lineno">  75</tt>  <tt class="py-line"><tt class="py-docstring">    FOL KB, something like ask(Brother(x, y)) might return many substitutions</tt> </tt>
<a name="L76"></a><tt class="py-lineno">  76</tt>  <tt class="py-line"><tt class="py-docstring">    such as {x: Cain, y: Abel}, {x: Abel, y: Cain}, {x: George, y: Jeb}, etc.  </tt> </tt>
<a name="L77"></a><tt class="py-lineno">  77</tt>  <tt class="py-line"><tt class="py-docstring">    So ask_generator generates these one at a time, and ask either returns the</tt> </tt>
<a name="L78"></a><tt class="py-lineno">  78</tt>  <tt class="py-line"><tt class="py-docstring">    first one or returns False."""</tt> </tt>
<a name="L79"></a><tt class="py-lineno">  79</tt>  <tt class="py-line"> </tt>
<a name="KB.__init__"></a><div id="KB.__init__-def"><a name="L80"></a><tt class="py-lineno">  80</tt> <a class="py-toggle" href="#" id="KB.__init__-toggle" onclick="return toggle('KB.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.KB-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="KB.__init__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="KB.__init__-expanded"><a name="L81"></a><tt class="py-lineno">  81</tt>  <tt class="py-line">        <tt class="py-name">abstract</tt> </tt>
</div><a name="L82"></a><tt class="py-lineno">  82</tt>  <tt class="py-line"> </tt>
<a name="KB.tell"></a><div id="KB.tell-def"><a name="L83"></a><tt class="py-lineno">  83</tt> <a class="py-toggle" href="#" id="KB.tell-toggle" onclick="return toggle('KB.tell');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.KB-class.html#tell">tell</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
</div><a name="L84"></a><tt class="py-lineno">  84</tt>  <tt class="py-line">        <tt class="py-docstring">"Add the sentence to the KB"</tt> </tt>
<a name="L85"></a><tt class="py-lineno">  85</tt>  <tt class="py-line">        <tt class="py-name">abstract</tt> </tt>
</div><a name="L86"></a><tt class="py-lineno">  86</tt>  <tt class="py-line"> </tt>
<a name="KB.ask"></a><div id="KB.ask-def"><a name="L87"></a><tt class="py-lineno">  87</tt> <a class="py-toggle" href="#" id="KB.ask-toggle" onclick="return toggle('KB.ask');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.KB-class.html#ask">ask</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="KB.ask-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="KB.ask-expanded"><a name="L88"></a><tt class="py-lineno">  88</tt>  <tt class="py-line">        <tt class="py-docstring">"""Ask returns a substitution that makes the query true, or</tt> </tt>
<a name="L89"></a><tt class="py-lineno">  89</tt>  <tt class="py-line"><tt class="py-docstring">        it returns False. It is implemented in terms of ask_generator."""</tt> </tt>
<a name="L90"></a><tt class="py-lineno">  90</tt>  <tt class="py-line">        <tt class="py-keyword">try</tt><tt class="py-op">:</tt>  </tt>
<a name="L91"></a><tt class="py-lineno">  91</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-10" class="py-name" targets="Method spade.logic.FolKB.ask_generator()=spade.logic.FolKB-class.html#ask_generator,Method spade.logic.KB.ask_generator()=spade.logic.KB-class.html#ask_generator,Method spade.logic.PropHornKB.ask_generator()=spade.logic.PropHornKB-class.html#ask_generator,Method spade.logic.PropKB.ask_generator()=spade.logic.PropKB-class.html#ask_generator"><a title="spade.logic.FolKB.ask_generator
spade.logic.KB.ask_generator
spade.logic.PropHornKB.ask_generator
spade.logic.PropKB.ask_generator" class="py-name" href="#" onclick="return doclink('link-10', 'ask_generator', 'link-10');">ask_generator</a></tt><tt class="py-op">(</tt><tt class="py-name">query</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">next</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L92"></a><tt class="py-lineno">  92</tt>  <tt class="py-line">        <tt class="py-keyword">except</tt> <tt class="py-name">StopIteration</tt><tt class="py-op">:</tt> </tt>
<a name="L93"></a><tt class="py-lineno">  93</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
</div><a name="L94"></a><tt class="py-lineno">  94</tt>  <tt class="py-line"> </tt>
<a name="KB.ask_generator"></a><div id="KB.ask_generator-def"><a name="L95"></a><tt class="py-lineno">  95</tt> <a class="py-toggle" href="#" id="KB.ask_generator-toggle" onclick="return toggle('KB.ask_generator');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.KB-class.html#ask_generator">ask_generator</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
</div><a name="L96"></a><tt class="py-lineno">  96</tt>  <tt class="py-line">        <tt class="py-docstring">"Yield all the substitutions that make query true."</tt> </tt>
<a name="L97"></a><tt class="py-lineno">  97</tt>  <tt class="py-line">        <tt class="py-name">abstract</tt> </tt>
</div><a name="L98"></a><tt class="py-lineno">  98</tt>  <tt class="py-line"> </tt>
<a name="KB.retract"></a><div id="KB.retract-def"><a name="L99"></a><tt class="py-lineno">  99</tt> <a class="py-toggle" href="#" id="KB.retract-toggle" onclick="return toggle('KB.retract');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.KB-class.html#retract">retract</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="KB.retract-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="KB.retract-expanded"><a name="L100"></a><tt class="py-lineno"> 100</tt>  <tt class="py-line">        <tt class="py-docstring">"Remove the sentence from the KB"</tt> </tt>
<a name="L101"></a><tt class="py-lineno"> 101</tt>  <tt class="py-line">        <tt class="py-name">abstract</tt> </tt>
</div></div><a name="L102"></a><tt class="py-lineno"> 102</tt>  <tt class="py-line"> </tt>
<a name="L103"></a><tt class="py-lineno"> 103</tt>  <tt class="py-line"> </tt>
<a name="PropKB"></a><div id="PropKB-def"><a name="L104"></a><tt class="py-lineno"> 104</tt> <a class="py-toggle" href="#" id="PropKB-toggle" onclick="return toggle('PropKB');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="spade.logic.PropKB-class.html">PropKB</a><tt class="py-op">(</tt><tt class="py-base-class">KB</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropKB-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="PropKB-expanded"><a name="L105"></a><tt class="py-lineno"> 105</tt>  <tt class="py-line">    <tt class="py-docstring">"A KB for Propositional Logic.  Inefficient, with no indexing."</tt> </tt>
<a name="L106"></a><tt class="py-lineno"> 106</tt>  <tt class="py-line"> </tt>
<a name="PropKB.__init__"></a><div id="PropKB.__init__-def"><a name="L107"></a><tt class="py-lineno"> 107</tt> <a class="py-toggle" href="#" id="PropKB.__init__-toggle" onclick="return toggle('PropKB.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropKB-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">=</tt><tt class="py-name">None</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropKB.__init__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="PropKB.__init__-expanded"><a name="L108"></a><tt class="py-lineno"> 108</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L109"></a><tt class="py-lineno"> 109</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">sentence</tt><tt class="py-op">:</tt> </tt>
<a name="L110"></a><tt class="py-lineno"> 110</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-11" class="py-name" targets="Method spade.logic.FolKB.tell()=spade.logic.FolKB-class.html#tell,Method spade.logic.KB.tell()=spade.logic.KB-class.html#tell,Method spade.logic.PropHornKB.tell()=spade.logic.PropHornKB-class.html#tell,Method spade.logic.PropKB.tell()=spade.logic.PropKB-class.html#tell"><a title="spade.logic.FolKB.tell
spade.logic.KB.tell
spade.logic.PropHornKB.tell
spade.logic.PropKB.tell" class="py-name" href="#" onclick="return doclink('link-11', 'tell', 'link-11');">tell</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt> </tt>
</div><a name="L111"></a><tt class="py-lineno"> 111</tt>  <tt class="py-line"> </tt>
<a name="PropKB.tell"></a><div id="PropKB.tell-def"><a name="L112"></a><tt class="py-lineno"> 112</tt> <a class="py-toggle" href="#" id="PropKB.tell-toggle" onclick="return toggle('PropKB.tell');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropKB-class.html#tell">tell</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
</div><a name="L113"></a><tt class="py-lineno"> 113</tt>  <tt class="py-line">        <tt class="py-docstring">"Add the sentence's clauses to the KB"</tt> </tt>
<a name="L114"></a><tt class="py-lineno"> 114</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt id="link-12" class="py-name" targets="Function spade.logic.extend()=spade.logic-module.html#extend"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-12', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt id="link-13" class="py-name" targets="Function spade.logic.conjuncts()=spade.logic-module.html#conjuncts"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-13', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-14" class="py-name" targets="Function spade.logic.to_cnf()=spade.logic-module.html#to_cnf"><a title="spade.logic.to_cnf" class="py-name" href="#" onclick="return doclink('link-14', 'to_cnf', 'link-14');">to_cnf</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt>         </tt>
</div><a name="L115"></a><tt class="py-lineno"> 115</tt>  <tt class="py-line"> </tt>
<a name="PropKB.ask_generator"></a><div id="PropKB.ask_generator-def"><a name="L116"></a><tt class="py-lineno"> 116</tt> <a class="py-toggle" href="#" id="PropKB.ask_generator-toggle" onclick="return toggle('PropKB.ask_generator');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropKB-class.html#ask_generator">ask_generator</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
</div><a name="L117"></a><tt class="py-lineno"> 117</tt>  <tt class="py-line">        <tt class="py-docstring">"Yield the empty substitution if KB implies query; else False"</tt> </tt>
<a name="L118"></a><tt class="py-lineno"> 118</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt id="link-15" class="py-name" targets="Function spade.logic.tt_entails()=spade.logic-module.html#tt_entails"><a title="spade.logic.tt_entails" class="py-name" href="#" onclick="return doclink('link-15', 'tt_entails', 'link-15');">tt_entails</a></tt><tt class="py-op">(</tt><tt id="link-16" class="py-name" targets="Class spade.logic.Expr=spade.logic.Expr-class.html"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-16', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L119"></a><tt class="py-lineno"> 119</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> </tt>
<a name="L120"></a><tt class="py-lineno"> 120</tt>  <tt class="py-line">        <tt class="py-keyword">yield</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
</div><a name="L121"></a><tt class="py-lineno"> 121</tt>  <tt class="py-line"> </tt>
<a name="PropKB.retract"></a><div id="PropKB.retract-def"><a name="L122"></a><tt class="py-lineno"> 122</tt> <a class="py-toggle" href="#" id="PropKB.retract-toggle" onclick="return toggle('PropKB.retract');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropKB-class.html#retract">retract</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropKB.retract-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="PropKB.retract-expanded"><a name="L123"></a><tt class="py-lineno"> 123</tt>  <tt class="py-line">        <tt class="py-docstring">"Remove the sentence's clauses from the KB"</tt> </tt>
<a name="L124"></a><tt class="py-lineno"> 124</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt id="link-17" class="py-name" targets="Variable spade.ACLParser.c=spade.ACLParser-module.html#c,Variable spade.AMS.c=spade.AMS-module.html#c,Variable spade.DF.c=spade.DF-module.html#c,Variable spade.SL0Parser.c=spade.SL0Parser-module.html#c,Variable spade.pyparsing.c=spade.pyparsing-module.html#c"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-17', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt id="link-18" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-18', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-19" class="py-name"><a title="spade.logic.to_cnf" class="py-name" href="#" onclick="return doclink('link-19', 'to_cnf', 'link-14');">to_cnf</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L125"></a><tt class="py-lineno"> 125</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-20" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-20', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L126"></a><tt class="py-lineno"> 126</tt>  <tt class="py-line">                <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt class="py-name">remove</tt><tt class="py-op">(</tt><tt id="link-21" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-21', 'c', 'link-17');">c</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L127"></a><tt class="py-lineno"> 127</tt>  <tt class="py-line"> </tt>
<a name="L128"></a><tt class="py-lineno"> 128</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L129"></a><tt class="py-lineno"> 129</tt>  <tt class="py-line">     </tt>
<a name="L130"></a><tt class="py-lineno"> 130</tt>  <tt class="py-line"><tt class="py-comment">#class KB_Agent(agents.Agent):</tt> </tt>
<a name="L131"></a><tt class="py-lineno"> 131</tt>  <tt class="py-line">    <tt class="py-string">"""A generic logical knowledge-based agent. [Fig. 7.1]"""</tt> </tt>
<a name="L132"></a><tt class="py-lineno"> 132</tt>  <tt class="py-line">    <tt class="py-string">"""def __init__(self, KB):</tt> </tt>
<a name="L133"></a><tt class="py-lineno"> 133</tt>  <tt class="py-line"><tt class="py-string">        t = 0</tt> </tt>
<a name="L134"></a><tt class="py-lineno"> 134</tt>  <tt class="py-line"><tt class="py-string">        def program(percept):</tt> </tt>
<a name="L135"></a><tt class="py-lineno"> 135</tt>  <tt class="py-line"><tt class="py-string">            KB.tell(self.make_percept_sentence(percept, t))</tt> </tt>
<a name="L136"></a><tt class="py-lineno"> 136</tt>  <tt class="py-line"><tt class="py-string">            action = KB.ask(self.make_action_query(t))</tt> </tt>
<a name="L137"></a><tt class="py-lineno"> 137</tt>  <tt class="py-line"><tt class="py-string">            KB.tell(self.make_action_sentence(action, t))</tt> </tt>
<a name="L138"></a><tt class="py-lineno"> 138</tt>  <tt class="py-line"><tt class="py-string">            t = t + 1</tt> </tt>
<a name="L139"></a><tt class="py-lineno"> 139</tt>  <tt class="py-line"><tt class="py-string">            return action</tt> </tt>
<a name="L140"></a><tt class="py-lineno"> 140</tt>  <tt class="py-line"><tt class="py-string">        self.program = program</tt> </tt>
<a name="L141"></a><tt class="py-lineno"> 141</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L142"></a><tt class="py-lineno"> 142</tt>  <tt class="py-line"><tt class="py-string">    def make_percept_sentence(self, percept, t): </tt> </tt>
<a name="L143"></a><tt class="py-lineno"> 143</tt>  <tt class="py-line"><tt class="py-string">        return(Expr("Percept")(percept, t))</tt> </tt>
<a name="L144"></a><tt class="py-lineno"> 144</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L145"></a><tt class="py-lineno"> 145</tt>  <tt class="py-line"><tt class="py-string">    def make_action_query(self, t): </tt> </tt>
<a name="L146"></a><tt class="py-lineno"> 146</tt>  <tt class="py-line"><tt class="py-string">        return(expr("ShouldDo(action, %d)" % t))</tt> </tt>
<a name="L147"></a><tt class="py-lineno"> 147</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L148"></a><tt class="py-lineno"> 148</tt>  <tt class="py-line"><tt class="py-string">    def make_action_sentence(self, action, t):</tt> </tt>
<a name="L149"></a><tt class="py-lineno"> 149</tt>  <tt class="py-line"><tt class="py-string">        return(Expr("Did")(action, t))"""</tt> </tt>
</div><a name="L150"></a><tt class="py-lineno"> 150</tt>  <tt class="py-line"> </tt>
<a name="L151"></a><tt class="py-lineno"> 151</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L152"></a><tt class="py-lineno"> 152</tt>  <tt class="py-line"> </tt>
<a name="Expr"></a><div id="Expr-def"><a name="L153"></a><tt class="py-lineno"> 153</tt> <a class="py-toggle" href="#" id="Expr-toggle" onclick="return toggle('Expr');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="spade.logic.Expr-class.html">Expr</a><tt class="py-op">:</tt> </tt>
</div><div id="Expr-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="Expr-expanded"><a name="L154"></a><tt class="py-lineno"> 154</tt>  <tt class="py-line">    <tt class="py-docstring">"""A symbolic mathematical expression.  We use this class for logical</tt> </tt>
<a name="L155"></a><tt class="py-lineno"> 155</tt>  <tt class="py-line"><tt class="py-docstring">    expressions, and for terms within logical expressions. In general, an</tt> </tt>
<a name="L156"></a><tt class="py-lineno"> 156</tt>  <tt class="py-line"><tt class="py-docstring">    Expr has an op (operator) and a list of args.  The op can be:</tt> </tt>
<a name="L157"></a><tt class="py-lineno"> 157</tt>  <tt class="py-line"><tt class="py-docstring">      Null-ary (no args) op:</tt> </tt>
<a name="L158"></a><tt class="py-lineno"> 158</tt>  <tt class="py-line"><tt class="py-docstring">        A number, representing the number itself.  (e.g. Expr(42) =&gt; 42)</tt> </tt>
<a name="L159"></a><tt class="py-lineno"> 159</tt>  <tt class="py-line"><tt class="py-docstring">        A symbol, representing a variable or constant (e.g. Expr('F') =&gt; F)</tt> </tt>
<a name="L160"></a><tt class="py-lineno"> 160</tt>  <tt class="py-line"><tt class="py-docstring">      Unary (1 arg) op:</tt> </tt>
<a name="L161"></a><tt class="py-lineno"> 161</tt>  <tt class="py-line"><tt class="py-docstring">        '~', '-', representing NOT, negation (e.g. Expr('~', Expr('P')) =&gt; ~P)</tt> </tt>
<a name="L162"></a><tt class="py-lineno"> 162</tt>  <tt class="py-line"><tt class="py-docstring">      Binary (2 arg) op:</tt> </tt>
<a name="L163"></a><tt class="py-lineno"> 163</tt>  <tt class="py-line"><tt class="py-docstring">        '&gt;&gt;', '&lt;&lt;', representing forward and backward implication</tt> </tt>
<a name="L164"></a><tt class="py-lineno"> 164</tt>  <tt class="py-line"><tt class="py-docstring">        '+', '-', '*', '/', '**', representing arithmetic operators</tt> </tt>
<a name="L165"></a><tt class="py-lineno"> 165</tt>  <tt class="py-line"><tt class="py-docstring">        '&lt;', '&gt;', '&gt;=', '&lt;=', representing comparison operators</tt> </tt>
<a name="L166"></a><tt class="py-lineno"> 166</tt>  <tt class="py-line"><tt class="py-docstring">        '&lt;=&gt;', '^', representing logical equality and XOR</tt> </tt>
<a name="L167"></a><tt class="py-lineno"> 167</tt>  <tt class="py-line"><tt class="py-docstring">      N-ary (0 or more args) op:</tt> </tt>
<a name="L168"></a><tt class="py-lineno"> 168</tt>  <tt class="py-line"><tt class="py-docstring">        '&amp;', '|', representing conjunction and disjunction</tt> </tt>
<a name="L169"></a><tt class="py-lineno"> 169</tt>  <tt class="py-line"><tt class="py-docstring">        A symbol, representing a function term or FOL proposition</tt> </tt>
<a name="L170"></a><tt class="py-lineno"> 170</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L171"></a><tt class="py-lineno"> 171</tt>  <tt class="py-line"><tt class="py-docstring">    Exprs can be constructed with operator overloading: if x and y are Exprs,</tt> </tt>
<a name="L172"></a><tt class="py-lineno"> 172</tt>  <tt class="py-line"><tt class="py-docstring">    then so are x + y and x &amp; y, etc.  Also, if F and x are Exprs, then so is </tt> </tt>
<a name="L173"></a><tt class="py-lineno"> 173</tt>  <tt class="py-line"><tt class="py-docstring">    F(x); it works by overloading the __call__ method of the Expr F.  Note </tt> </tt>
<a name="L174"></a><tt class="py-lineno"> 174</tt>  <tt class="py-line"><tt class="py-docstring">    that in the Expr that is created by F(x), the op is the str 'F', not the </tt> </tt>
<a name="L175"></a><tt class="py-lineno"> 175</tt>  <tt class="py-line"><tt class="py-docstring">    Expr F.   See http://www.python.org/doc/current/ref/specialnames.html </tt> </tt>
<a name="L176"></a><tt class="py-lineno"> 176</tt>  <tt class="py-line"><tt class="py-docstring">    to learn more about operator overloading in Python.</tt> </tt>
<a name="L177"></a><tt class="py-lineno"> 177</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L178"></a><tt class="py-lineno"> 178</tt>  <tt class="py-line"><tt class="py-docstring">    WARNING: x == y and x != y are NOT Exprs.  The reason is that we want</tt> </tt>
<a name="L179"></a><tt class="py-lineno"> 179</tt>  <tt class="py-line"><tt class="py-docstring">    to write code that tests 'if x == y:' and if x == y were the same</tt> </tt>
<a name="L180"></a><tt class="py-lineno"> 180</tt>  <tt class="py-line"><tt class="py-docstring">    as Expr('==', x, y), then the result would always be true; not what a</tt> </tt>
<a name="L181"></a><tt class="py-lineno"> 181</tt>  <tt class="py-line"><tt class="py-docstring">    programmer would expect.  But we still need to form Exprs representing</tt> </tt>
<a name="L182"></a><tt class="py-lineno"> 182</tt>  <tt class="py-line"><tt class="py-docstring">    equalities and disequalities.  We concentrate on logical equality (or</tt> </tt>
<a name="L183"></a><tt class="py-lineno"> 183</tt>  <tt class="py-line"><tt class="py-docstring">    equivalence) and logical disequality (or XOR).  You have 3 choices:</tt> </tt>
<a name="L184"></a><tt class="py-lineno"> 184</tt>  <tt class="py-line"><tt class="py-docstring">        (1) Expr('&lt;=&gt;', x, y) and Expr('^', x, y)</tt> </tt>
<a name="L185"></a><tt class="py-lineno"> 185</tt>  <tt class="py-line"><tt class="py-docstring">            Note that ^ is bitwose XOR in Python (and Java and C++)</tt> </tt>
<a name="L186"></a><tt class="py-lineno"> 186</tt>  <tt class="py-line"><tt class="py-docstring">        (2) expr('x &lt;=&gt; y') and expr('x =/= y').  </tt> </tt>
<a name="L187"></a><tt class="py-lineno"> 187</tt>  <tt class="py-line"><tt class="py-docstring">            See the doc string for the function expr.</tt> </tt>
<a name="L188"></a><tt class="py-lineno"> 188</tt>  <tt class="py-line"><tt class="py-docstring">        (3) (x % y) and (x ^ y).</tt> </tt>
<a name="L189"></a><tt class="py-lineno"> 189</tt>  <tt class="py-line"><tt class="py-docstring">            It is very ugly to have (x % y) mean (x &lt;=&gt; y), but we need</tt> </tt>
<a name="L190"></a><tt class="py-lineno"> 190</tt>  <tt class="py-line"><tt class="py-docstring">            SOME operator to make (2) work, and this seems the best choice.</tt> </tt>
<a name="L191"></a><tt class="py-lineno"> 191</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L192"></a><tt class="py-lineno"> 192</tt>  <tt class="py-line"><tt class="py-docstring">    WARNING: if x is an Expr, then so is x + 1, because the int 1 gets</tt> </tt>
<a name="L193"></a><tt class="py-lineno"> 193</tt>  <tt class="py-line"><tt class="py-docstring">    coerced to an Expr by the constructor.  But 1 + x is an error, because</tt> </tt>
<a name="L194"></a><tt class="py-lineno"> 194</tt>  <tt class="py-line"><tt class="py-docstring">    1 doesn't know how to add an Expr.  (Adding an __radd__ method to Expr</tt> </tt>
<a name="L195"></a><tt class="py-lineno"> 195</tt>  <tt class="py-line"><tt class="py-docstring">    wouldn't help, because int.__add__ is still called first.) Therefore,</tt> </tt>
<a name="L196"></a><tt class="py-lineno"> 196</tt>  <tt class="py-line"><tt class="py-docstring">    you should use Expr(1) + x instead, or ONE + x, or expr('1 + x').</tt> </tt>
<a name="L197"></a><tt class="py-lineno"> 197</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L198"></a><tt class="py-lineno"> 198</tt>  <tt class="py-line"> </tt>
<a name="Expr.__init__"></a><div id="Expr.__init__-def"><a name="L199"></a><tt class="py-lineno"> 199</tt> <a class="py-toggle" href="#" id="Expr.__init__-toggle" onclick="return toggle('Expr.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">args</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Expr.__init__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Expr.__init__-expanded"><a name="L200"></a><tt class="py-lineno"> 200</tt>  <tt class="py-line">        <tt class="py-docstring">"Op is a string or number; args are Exprs (or are coerced to Exprs)."</tt> </tt>
<a name="L201"></a><tt class="py-lineno"> 201</tt>  <tt class="py-line">        <tt class="py-keyword">assert</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">str</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt id="link-22" class="py-name"><a title="spade.logic.isnumber" class="py-name" href="#" onclick="return doclink('link-22', 'isnumber', 'link-4');">isnumber</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L202"></a><tt class="py-lineno"> 202</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">=</tt> <tt id="link-23" class="py-name" targets="Function spade.logic.num_or_str()=spade.logic-module.html#num_or_str"><a title="spade.logic.num_or_str" class="py-name" href="#" onclick="return doclink('link-23', 'num_or_str', 'link-23');">num_or_str</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> </tt>
<a name="L203"></a><tt class="py-lineno"> 203</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-24" class="py-name" targets="Function spade.logic.expr()=spade.logic-module.html#expr"><a title="spade.logic.expr" class="py-name" href="#" onclick="return doclink('link-24', 'expr', 'link-24');">expr</a></tt><tt class="py-op">,</tt> <tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-comment">## Coerce args to Exprs</tt> </tt>
</div><a name="L204"></a><tt class="py-lineno"> 204</tt>  <tt class="py-line"> </tt>
<a name="Expr.__call__"></a><div id="Expr.__call__-def"><a name="L205"></a><tt class="py-lineno"> 205</tt> <a class="py-toggle" href="#" id="Expr.__call__-toggle" onclick="return toggle('Expr.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">args</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Expr.__call__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Expr.__call__-expanded"><a name="L206"></a><tt class="py-lineno"> 206</tt>  <tt class="py-line">        <tt class="py-docstring">"""Self must be a symbol with no args, such as Expr('F').  Create a new</tt> </tt>
<a name="L207"></a><tt class="py-lineno"> 207</tt>  <tt class="py-line"><tt class="py-docstring">        Expr with 'F' as op and the args as arguments."""</tt> </tt>
<a name="L208"></a><tt class="py-lineno"> 208</tt>  <tt class="py-line">        <tt class="py-keyword">assert</tt> <tt id="link-25" class="py-name" targets="Function spade.logic.is_symbol()=spade.logic-module.html#is_symbol"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-25', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> </tt>
<a name="L209"></a><tt class="py-lineno"> 209</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-26" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-26', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
</div><a name="L210"></a><tt class="py-lineno"> 210</tt>  <tt class="py-line"> </tt>
<a name="Expr.__repr__"></a><div id="Expr.__repr__-def"><a name="L211"></a><tt class="py-lineno"> 211</tt> <a class="py-toggle" href="#" id="Expr.__repr__-toggle" onclick="return toggle('Expr.__repr__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__repr__">__repr__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Expr.__repr__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Expr.__repr__-expanded"><a name="L212"></a><tt class="py-lineno"> 212</tt>  <tt class="py-line">        <tt class="py-docstring">"Show something like 'P' or 'P(x, y)', or '~P' or '(P | Q | R)'"</tt> </tt>
<a name="L213"></a><tt class="py-lineno"> 213</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> <tt class="py-comment"># Constant or proposition with arity 0</tt> </tt>
<a name="L214"></a><tt class="py-lineno"> 214</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">str</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> </tt>
<a name="L215"></a><tt class="py-lineno"> 215</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt id="link-27" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-27', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-comment"># Functional or Propositional operator</tt> </tt>
<a name="L216"></a><tt class="py-lineno"> 216</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-string">'%s(%s)'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-string">', '</tt><tt class="py-op">.</tt><tt class="py-name">join</tt><tt class="py-op">(</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt class="py-name">repr</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L217"></a><tt class="py-lineno"> 217</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> <tt class="py-comment"># Prefix operator</tt> </tt>
<a name="L218"></a><tt class="py-lineno"> 218</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">+</tt> <tt class="py-name">repr</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L219"></a><tt class="py-lineno"> 219</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-comment"># Infix operator</tt> </tt>
<a name="L220"></a><tt class="py-lineno"> 220</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-string">'(%s)'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-string">' '</tt><tt class="py-op">+</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">+</tt><tt class="py-string">' '</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">join</tt><tt class="py-op">(</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt class="py-name">repr</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L221"></a><tt class="py-lineno"> 221</tt>  <tt class="py-line"> </tt>
<a name="Expr.__eq__"></a><div id="Expr.__eq__-def"><a name="L222"></a><tt class="py-lineno"> 222</tt> <a class="py-toggle" href="#" id="Expr.__eq__-toggle" onclick="return toggle('Expr.__eq__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__eq__">__eq__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Expr.__eq__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Expr.__eq__-expanded"><a name="L223"></a><tt class="py-lineno"> 223</tt>  <tt class="py-line">        <tt class="py-docstring">"""x and y are equal iff their ops and args are equal."""</tt> </tt>
<a name="L224"></a><tt class="py-lineno"> 224</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-name">other</tt> <tt class="py-keyword">is</tt> <tt class="py-name">self</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">other</tt><tt class="py-op">,</tt> <tt id="link-28" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-28', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt>  </tt>
<a name="L225"></a><tt class="py-lineno"> 225</tt>  <tt class="py-line">            <tt class="py-keyword">and</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-name">other</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-keyword">and</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> <tt class="py-op">==</tt> <tt class="py-name">other</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
</div><a name="L226"></a><tt class="py-lineno"> 226</tt>  <tt class="py-line"> </tt>
<a name="Expr.__hash__"></a><div id="Expr.__hash__-def"><a name="L227"></a><tt class="py-lineno"> 227</tt> <a class="py-toggle" href="#" id="Expr.__hash__-toggle" onclick="return toggle('Expr.__hash__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__hash__">__hash__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Expr.__hash__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="Expr.__hash__-expanded"><a name="L228"></a><tt class="py-lineno"> 228</tt>  <tt class="py-line">        <tt class="py-docstring">"Need a hash method so Exprs can live in dicts."</tt> </tt>
<a name="L229"></a><tt class="py-lineno"> 229</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">hash</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> <tt class="py-op">^</tt> <tt class="py-name">hash</tt><tt class="py-op">(</tt><tt class="py-name">tuple</tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L230"></a><tt class="py-lineno"> 230</tt>  <tt class="py-line"> </tt>
<a name="L231"></a><tt class="py-lineno"> 231</tt>  <tt class="py-line">    <tt class="py-comment"># See http://www.python.org/doc/current/lib/module-operator.html</tt> </tt>
<a name="L232"></a><tt class="py-lineno"> 232</tt>  <tt class="py-line">    <tt class="py-comment"># Not implemented: not, abs, pos, concat, contains, *item, *slice</tt> </tt>
<a name="Expr.__lt__"></a><div id="Expr.__lt__-def"><a name="L233"></a><tt class="py-lineno"> 233</tt> <a class="py-toggle" href="#" id="Expr.__lt__-toggle" onclick="return toggle('Expr.__lt__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__lt__">__lt__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>     <tt class="py-keyword">return</tt> <tt id="link-29" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-29', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&lt;'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__le__"></a><div id="Expr.__le__-def"><a name="L234"></a><tt class="py-lineno"> 234</tt> <a class="py-toggle" href="#" id="Expr.__le__-toggle" onclick="return toggle('Expr.__le__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__le__">__le__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>     <tt class="py-keyword">return</tt> <tt id="link-30" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-30', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&lt;='</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__ge__"></a><div id="Expr.__ge__-def"><a name="L235"></a><tt class="py-lineno"> 235</tt> <a class="py-toggle" href="#" id="Expr.__ge__-toggle" onclick="return toggle('Expr.__ge__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__ge__">__ge__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>     <tt class="py-keyword">return</tt> <tt id="link-31" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-31', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&gt;='</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__gt__"></a><div id="Expr.__gt__-def"><a name="L236"></a><tt class="py-lineno"> 236</tt> <a class="py-toggle" href="#" id="Expr.__gt__-toggle" onclick="return toggle('Expr.__gt__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__gt__">__gt__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>     <tt class="py-keyword">return</tt> <tt id="link-32" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-32', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&gt;'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__add__"></a><div id="Expr.__add__-def"><a name="L237"></a><tt class="py-lineno"> 237</tt> <a class="py-toggle" href="#" id="Expr.__add__-toggle" onclick="return toggle('Expr.__add__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__add__">__add__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-33" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-33', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'+'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__sub__"></a><div id="Expr.__sub__-def"><a name="L238"></a><tt class="py-lineno"> 238</tt> <a class="py-toggle" href="#" id="Expr.__sub__-toggle" onclick="return toggle('Expr.__sub__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__sub__">__sub__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-34" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-34', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'-'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__and__"></a><div id="Expr.__and__-def"><a name="L239"></a><tt class="py-lineno"> 239</tt> <a class="py-toggle" href="#" id="Expr.__and__-toggle" onclick="return toggle('Expr.__and__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__and__">__and__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-35" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-35', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__div__"></a><div id="Expr.__div__-def"><a name="L240"></a><tt class="py-lineno"> 240</tt> <a class="py-toggle" href="#" id="Expr.__div__-toggle" onclick="return toggle('Expr.__div__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__div__">__div__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-36" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-36', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'/'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__truediv__"></a><div id="Expr.__truediv__-def"><a name="L241"></a><tt class="py-lineno"> 241</tt> <a class="py-toggle" href="#" id="Expr.__truediv__-toggle" onclick="return toggle('Expr.__truediv__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__truediv__">__truediv__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt><tt class="py-keyword">return</tt> <tt id="link-37" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-37', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'/'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__invert__"></a><div id="Expr.__invert__-def"><a name="L242"></a><tt class="py-lineno"> 242</tt> <a class="py-toggle" href="#" id="Expr.__invert__-toggle" onclick="return toggle('Expr.__invert__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__invert__">__invert__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>        <tt class="py-keyword">return</tt> <tt id="link-38" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-38', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'~'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__lshift__"></a><div id="Expr.__lshift__-def"><a name="L243"></a><tt class="py-lineno"> 243</tt> <a class="py-toggle" href="#" id="Expr.__lshift__-toggle" onclick="return toggle('Expr.__lshift__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__lshift__">__lshift__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-39" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-39', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&lt;&lt;'</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__rshift__"></a><div id="Expr.__rshift__-def"><a name="L244"></a><tt class="py-lineno"> 244</tt> <a class="py-toggle" href="#" id="Expr.__rshift__-toggle" onclick="return toggle('Expr.__rshift__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__rshift__">__rshift__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-40" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-40', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__mul__"></a><div id="Expr.__mul__-def"><a name="L245"></a><tt class="py-lineno"> 245</tt> <a class="py-toggle" href="#" id="Expr.__mul__-toggle" onclick="return toggle('Expr.__mul__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__mul__">__mul__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-41" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-41', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'*'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__neg__"></a><div id="Expr.__neg__-def"><a name="L246"></a><tt class="py-lineno"> 246</tt> <a class="py-toggle" href="#" id="Expr.__neg__-toggle" onclick="return toggle('Expr.__neg__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__neg__">__neg__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>           <tt class="py-keyword">return</tt> <tt id="link-42" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-42', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'-'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__or__"></a><div id="Expr.__or__-def"><a name="L247"></a><tt class="py-lineno"> 247</tt> <a class="py-toggle" href="#" id="Expr.__or__-toggle" onclick="return toggle('Expr.__or__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__or__">__or__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>     <tt class="py-keyword">return</tt> <tt id="link-43" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-43', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'|'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__pow__"></a><div id="Expr.__pow__-def"><a name="L248"></a><tt class="py-lineno"> 248</tt> <a class="py-toggle" href="#" id="Expr.__pow__-toggle" onclick="return toggle('Expr.__pow__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__pow__">__pow__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-44" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-44', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'**'</tt><tt class="py-op">,</tt> <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__xor__"></a><div id="Expr.__xor__-def"><a name="L249"></a><tt class="py-lineno"> 249</tt> <a class="py-toggle" href="#" id="Expr.__xor__-toggle" onclick="return toggle('Expr.__xor__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__xor__">__xor__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-45" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-45', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'^'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> </tt>
</div><a name="Expr.__mod__"></a><div id="Expr.__mod__-def"><a name="L250"></a><tt class="py-lineno"> 250</tt> <a class="py-toggle" href="#" id="Expr.__mod__-toggle" onclick="return toggle('Expr.__mod__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.Expr-class.html#__mod__">__mod__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">other</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>    <tt class="py-keyword">return</tt> <tt id="link-46" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-46', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&lt;=&gt;'</tt><tt class="py-op">,</tt>  <tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-name">other</tt><tt class="py-op">)</tt> <tt class="py-comment">## (x % y)</tt> </tt>
</div></div><a name="L251"></a><tt class="py-lineno"> 251</tt>  <tt class="py-line">     </tt>
<a name="L252"></a><tt class="py-lineno"> 252</tt>  <tt class="py-line"> </tt>
<a name="L253"></a><tt class="py-lineno"> 253</tt>  <tt class="py-line"> </tt>
<a name="expr"></a><div id="expr-def"><a name="L254"></a><tt class="py-lineno"> 254</tt> <a class="py-toggle" href="#" id="expr-toggle" onclick="return toggle('expr');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#expr">expr</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="expr-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="expr-expanded"><a name="L255"></a><tt class="py-lineno"> 255</tt>  <tt class="py-line">    <tt class="py-docstring">"""Create an Expr representing a logic expression by parsing the input</tt> </tt>
<a name="L256"></a><tt class="py-lineno"> 256</tt>  <tt class="py-line"><tt class="py-docstring">    string. Symbols and numbers are automatically converted to Exprs.</tt> </tt>
<a name="L257"></a><tt class="py-lineno"> 257</tt>  <tt class="py-line"><tt class="py-docstring">    In addition you can use alternative spellings of these operators:</tt> </tt>
<a name="L258"></a><tt class="py-lineno"> 258</tt>  <tt class="py-line"><tt class="py-docstring">      'x ==&gt; y'   parses as   (x &gt;&gt; y)    # Implication</tt> </tt>
<a name="L259"></a><tt class="py-lineno"> 259</tt>  <tt class="py-line"><tt class="py-docstring">      'x &lt;== y'   parses as   (x &lt;&lt; y)    # Reverse implication</tt> </tt>
<a name="L260"></a><tt class="py-lineno"> 260</tt>  <tt class="py-line"><tt class="py-docstring">      'x &lt;=&gt; y'   parses as   (x % y)     # Logical equivalence</tt> </tt>
<a name="L261"></a><tt class="py-lineno"> 261</tt>  <tt class="py-line"><tt class="py-docstring">      'x =/= y'   parses as   (x ^ y)     # Logical disequality (xor)</tt> </tt>
<a name="L262"></a><tt class="py-lineno"> 262</tt>  <tt class="py-line"><tt class="py-docstring">    But BE CAREFUL; precedence of implication is wrong. expr('P &amp; Q ==&gt; R &amp; S')</tt> </tt>
<a name="L263"></a><tt class="py-lineno"> 263</tt>  <tt class="py-line"><tt class="py-docstring">    is ((P &amp; (Q &gt;&gt; R)) &amp; S); so you must use expr('(P &amp; Q) ==&gt; (R &amp; S)').</tt> </tt>
<a name="L264"></a><tt class="py-lineno"> 264</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; expr('P &lt;=&gt; Q(1)')</tt> </tt>
<a name="L265"></a><tt class="py-lineno"> 265</tt>  <tt class="py-line"><tt class="py-docstring">    (P &lt;=&gt; Q(1))</tt> </tt>
<a name="L266"></a><tt class="py-lineno"> 266</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; expr('P &amp; Q | ~R(x, F(x))')</tt> </tt>
<a name="L267"></a><tt class="py-lineno"> 267</tt>  <tt class="py-line"><tt class="py-docstring">    ((P &amp; Q) | ~R(x, F(x)))</tt> </tt>
<a name="L268"></a><tt class="py-lineno"> 268</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L269"></a><tt class="py-lineno"> 269</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt id="link-47" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-47', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">s</tt> </tt>
<a name="L270"></a><tt class="py-lineno"> 270</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-48" class="py-name"><a title="spade.logic.isnumber" class="py-name" href="#" onclick="return doclink('link-48', 'isnumber', 'link-4');">isnumber</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-49" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-49', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L271"></a><tt class="py-lineno"> 271</tt>  <tt class="py-line">    <tt class="py-comment">## Replace the alternative spellings of operators with canonical spellings</tt> </tt>
<a name="L272"></a><tt class="py-lineno"> 272</tt>  <tt class="py-line">    <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt><tt class="py-string">'==&gt;'</tt><tt class="py-op">,</tt> <tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt><tt class="py-string">'&lt;=='</tt><tt class="py-op">,</tt> <tt class="py-string">'&lt;&lt;'</tt><tt class="py-op">)</tt> </tt>
<a name="L273"></a><tt class="py-lineno"> 273</tt>  <tt class="py-line">    <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt><tt class="py-string">'&lt;=&gt;'</tt><tt class="py-op">,</tt> <tt class="py-string">'%'</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt class="py-name">replace</tt><tt class="py-op">(</tt><tt class="py-string">'=/='</tt><tt class="py-op">,</tt> <tt class="py-string">'^'</tt><tt class="py-op">)</tt> </tt>
<a name="L274"></a><tt class="py-lineno"> 274</tt>  <tt class="py-line">    <tt class="py-comment">## Replace a symbol or number, such as 'P' with 'Expr("P")'</tt> </tt>
<a name="L275"></a><tt class="py-lineno"> 275</tt>  <tt class="py-line">    <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt class="py-name">re</tt><tt class="py-op">.</tt><tt class="py-name">sub</tt><tt class="py-op">(</tt><tt class="py-string">r'([a-zA-Z0-9_.]+)'</tt><tt class="py-op">,</tt> <tt class="py-string">r'Expr("\1")'</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L276"></a><tt class="py-lineno"> 276</tt>  <tt class="py-line">    <tt class="py-comment">## Now eval the string.  (A security hole; do not use with an adversary.)</tt> </tt>
<a name="L277"></a><tt class="py-lineno"> 277</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-50" class="py-name" targets="Method spade.pyratemp.PseudoSandbox.eval()=spade.pyratemp.PseudoSandbox-class.html#eval"><a title="spade.pyratemp.PseudoSandbox.eval" class="py-name" href="#" onclick="return doclink('link-50', 'eval', 'link-50');">eval</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-op">{</tt><tt class="py-string">'Expr'</tt><tt class="py-op">:</tt><tt id="link-51" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-51', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">}</tt><tt class="py-op">)</tt> </tt>
</div><a name="L278"></a><tt class="py-lineno"> 278</tt>  <tt class="py-line"> </tt>
<a name="is_symbol"></a><div id="is_symbol-def"><a name="L279"></a><tt class="py-lineno"> 279</tt> <a class="py-toggle" href="#" id="is_symbol-toggle" onclick="return toggle('is_symbol');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_symbol">is_symbol</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_symbol-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_symbol-expanded"><a name="L280"></a><tt class="py-lineno"> 280</tt>  <tt class="py-line">    <tt class="py-docstring">"A string s is a symbol if it starts with an alphabetic char."</tt> </tt>
<a name="L281"></a><tt class="py-lineno"> 281</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">str</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">isalpha</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L282"></a><tt class="py-lineno"> 282</tt>  <tt class="py-line"> </tt>
<a name="is_var_symbol"></a><div id="is_var_symbol-def"><a name="L283"></a><tt class="py-lineno"> 283</tt> <a class="py-toggle" href="#" id="is_var_symbol-toggle" onclick="return toggle('is_var_symbol');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_var_symbol">is_var_symbol</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_var_symbol-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_var_symbol-expanded"><a name="L284"></a><tt class="py-lineno"> 284</tt>  <tt class="py-line">    <tt class="py-docstring">"A logic variable symbol is an initial-lowercase string."</tt> </tt>
<a name="L285"></a><tt class="py-lineno"> 285</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-52" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-52', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">islower</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L286"></a><tt class="py-lineno"> 286</tt>  <tt class="py-line"> </tt>
<a name="is_prop_symbol"></a><div id="is_prop_symbol-def"><a name="L287"></a><tt class="py-lineno"> 287</tt> <a class="py-toggle" href="#" id="is_prop_symbol-toggle" onclick="return toggle('is_prop_symbol');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_prop_symbol">is_prop_symbol</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_prop_symbol-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_prop_symbol-expanded"><a name="L288"></a><tt class="py-lineno"> 288</tt>  <tt class="py-line">    <tt class="py-docstring">"""A proposition logic symbol is an initial-uppercase string other than</tt> </tt>
<a name="L289"></a><tt class="py-lineno"> 289</tt>  <tt class="py-line"><tt class="py-docstring">    TRUE or FALSE."""</tt> </tt>
<a name="L290"></a><tt class="py-lineno"> 290</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-53" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-53', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">.</tt><tt class="py-name">isupper</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt> <tt class="py-op">!=</tt> <tt class="py-string">'TRUE'</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt> <tt class="py-op">!=</tt> <tt class="py-string">'FALSE'</tt> </tt>
</div><a name="L291"></a><tt class="py-lineno"> 291</tt>  <tt class="py-line"> </tt>
<a name="is_positive"></a><div id="is_positive-def"><a name="L292"></a><tt class="py-lineno"> 292</tt> <a class="py-toggle" href="#" id="is_positive-toggle" onclick="return toggle('is_positive');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_positive">is_positive</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_positive-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_positive-expanded"><a name="L293"></a><tt class="py-lineno"> 293</tt>  <tt class="py-line">    <tt class="py-docstring">"""s is an unnegated logical expression</tt> </tt>
<a name="L294"></a><tt class="py-lineno"> 294</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_positive(expr('F(A, B)'))</tt> </tt>
<a name="L295"></a><tt class="py-lineno"> 295</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L296"></a><tt class="py-lineno"> 296</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_positive(expr('~F(A, B)'))</tt> </tt>
<a name="L297"></a><tt class="py-lineno"> 297</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L298"></a><tt class="py-lineno"> 298</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L299"></a><tt class="py-lineno"> 299</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">!=</tt> <tt class="py-string">'~'</tt> </tt>
</div><a name="L300"></a><tt class="py-lineno"> 300</tt>  <tt class="py-line"> </tt>
<a name="is_negative"></a><div id="is_negative-def"><a name="L301"></a><tt class="py-lineno"> 301</tt> <a class="py-toggle" href="#" id="is_negative-toggle" onclick="return toggle('is_negative');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_negative">is_negative</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_negative-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_negative-expanded"><a name="L302"></a><tt class="py-lineno"> 302</tt>  <tt class="py-line">    <tt class="py-docstring">"""s is a negated logical expression</tt> </tt>
<a name="L303"></a><tt class="py-lineno"> 303</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_negative(expr('F(A, B)'))</tt> </tt>
<a name="L304"></a><tt class="py-lineno"> 304</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L305"></a><tt class="py-lineno"> 305</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_negative(expr('~F(A, B)'))</tt> </tt>
<a name="L306"></a><tt class="py-lineno"> 306</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L307"></a><tt class="py-lineno"> 307</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L308"></a><tt class="py-lineno"> 308</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'~'</tt> </tt>
</div><a name="L309"></a><tt class="py-lineno"> 309</tt>  <tt class="py-line"> </tt>
<a name="is_literal"></a><div id="is_literal-def"><a name="L310"></a><tt class="py-lineno"> 310</tt> <a class="py-toggle" href="#" id="is_literal-toggle" onclick="return toggle('is_literal');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_literal">is_literal</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_literal-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_literal-expanded"><a name="L311"></a><tt class="py-lineno"> 311</tt>  <tt class="py-line">    <tt class="py-docstring">"""s is a FOL literal</tt> </tt>
<a name="L312"></a><tt class="py-lineno"> 312</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_literal(expr('~F(A, B)'))</tt> </tt>
<a name="L313"></a><tt class="py-lineno"> 313</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L314"></a><tt class="py-lineno"> 314</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_literal(expr('F(A, B)'))</tt> </tt>
<a name="L315"></a><tt class="py-lineno"> 315</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L316"></a><tt class="py-lineno"> 316</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_literal(expr('F(A, B) &amp; G(B, C)'))</tt> </tt>
<a name="L317"></a><tt class="py-lineno"> 317</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L318"></a><tt class="py-lineno"> 318</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L319"></a><tt class="py-lineno"> 319</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-54" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-54', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'~'</tt> <tt class="py-keyword">and</tt> <tt id="link-55" class="py-name" targets="Function spade.logic.is_literal()=spade.logic-module.html#is_literal"><a title="spade.logic.is_literal" class="py-name" href="#" onclick="return doclink('link-55', 'is_literal', 'link-55');">is_literal</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L320"></a><tt class="py-lineno"> 320</tt>  <tt class="py-line"> </tt>
<a name="literals"></a><div id="literals-def"><a name="L321"></a><tt class="py-lineno"> 321</tt> <a class="py-toggle" href="#" id="literals-toggle" onclick="return toggle('literals');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#literals">literals</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="literals-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="literals-expanded"><a name="L322"></a><tt class="py-lineno"> 322</tt>  <tt class="py-line">    <tt class="py-docstring">"""returns the list of literals of logical expression s.</tt> </tt>
<a name="L323"></a><tt class="py-lineno"> 323</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; literals(expr('F(A, B)'))</tt> </tt>
<a name="L324"></a><tt class="py-lineno"> 324</tt>  <tt class="py-line"><tt class="py-docstring">    [F(A, B)]</tt> </tt>
<a name="L325"></a><tt class="py-lineno"> 325</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; literals(expr('~F(A, B)'))</tt> </tt>
<a name="L326"></a><tt class="py-lineno"> 326</tt>  <tt class="py-line"><tt class="py-docstring">    [~F(A, B)]</tt> </tt>
<a name="L327"></a><tt class="py-lineno"> 327</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; literals(expr('(F(A, B) &amp; G(B, C)) ==&gt; R(A, C)'))</tt> </tt>
<a name="L328"></a><tt class="py-lineno"> 328</tt>  <tt class="py-line"><tt class="py-docstring">    [F(A, B), G(B, C), R(A, C)]</tt> </tt>
<a name="L329"></a><tt class="py-lineno"> 329</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L330"></a><tt class="py-lineno"> 330</tt>  <tt class="py-line">    <tt class="py-name">op</tt> <tt class="py-op">=</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> </tt>
<a name="L331"></a><tt class="py-lineno"> 331</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">op</tt> <tt class="py-keyword">in</tt> <tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">,</tt> <tt class="py-string">'|'</tt><tt class="py-op">,</tt> <tt class="py-string">'&lt;&lt;'</tt><tt class="py-op">,</tt> <tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">,</tt> <tt class="py-string">'%'</tt><tt class="py-op">,</tt> <tt class="py-string">'^'</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L332"></a><tt class="py-lineno"> 332</tt>  <tt class="py-line">        <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L333"></a><tt class="py-lineno"> 333</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">arg</tt> <tt class="py-keyword">in</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">:</tt> </tt>
<a name="L334"></a><tt class="py-lineno"> 334</tt>  <tt class="py-line">            <tt class="py-name">result</tt><tt class="py-op">.</tt><tt id="link-56" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-56', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt id="link-57" class="py-name" targets="Function spade.logic.literals()=spade.logic-module.html#literals"><a title="spade.logic.literals" class="py-name" href="#" onclick="return doclink('link-57', 'literals', 'link-57');">literals</a></tt><tt class="py-op">(</tt><tt class="py-name">arg</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L335"></a><tt class="py-lineno"> 335</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">result</tt> </tt>
<a name="L336"></a><tt class="py-lineno"> 336</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-58" class="py-name"><a title="spade.logic.is_literal" class="py-name" href="#" onclick="return doclink('link-58', 'is_literal', 'link-55');">is_literal</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L337"></a><tt class="py-lineno"> 337</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt class="py-name">s</tt><tt class="py-op">]</tt> </tt>
<a name="L338"></a><tt class="py-lineno"> 338</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L339"></a><tt class="py-lineno"> 339</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
</div><a name="L340"></a><tt class="py-lineno"> 340</tt>  <tt class="py-line"> </tt>
<a name="variables"></a><div id="variables-def"><a name="L341"></a><tt class="py-lineno"> 341</tt> <a class="py-toggle" href="#" id="variables-toggle" onclick="return toggle('variables');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#variables">variables</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="variables-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="variables-expanded"><a name="L342"></a><tt class="py-lineno"> 342</tt>  <tt class="py-line">    <tt class="py-docstring">"""returns the set of variables in logical expression s.</tt> </tt>
<a name="L343"></a><tt class="py-lineno"> 343</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppset(variables(F(x, A, y)))</tt> </tt>
<a name="L344"></a><tt class="py-lineno"> 344</tt>  <tt class="py-line"><tt class="py-docstring">    set([x, y])</tt> </tt>
<a name="L345"></a><tt class="py-lineno"> 345</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppset(variables(expr('F(x, x) &amp; G(x, y) &amp; H(y, z) &amp; R(A, z, z)')))</tt> </tt>
<a name="L346"></a><tt class="py-lineno"> 346</tt>  <tt class="py-line"><tt class="py-docstring">    set([x, y, z])</tt> </tt>
<a name="L347"></a><tt class="py-lineno"> 347</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L348"></a><tt class="py-lineno"> 348</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-59" class="py-name"><a title="spade.logic.is_literal" class="py-name" href="#" onclick="return doclink('link-59', 'is_literal', 'link-55');">is_literal</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L349"></a><tt class="py-lineno"> 349</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">v</tt> <tt class="py-keyword">for</tt> <tt class="py-name">v</tt> <tt class="py-keyword">in</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> <tt class="py-keyword">if</tt> <tt id="link-60" class="py-name" targets="Function spade.logic.is_variable()=spade.logic-module.html#is_variable"><a title="spade.logic.is_variable" class="py-name" href="#" onclick="return doclink('link-60', 'is_variable', 'link-60');">is_variable</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L350"></a><tt class="py-lineno"> 350</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L351"></a><tt class="py-lineno"> 351</tt>  <tt class="py-line">        <tt class="py-name">vars</tt> <tt class="py-op">=</tt> <tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L352"></a><tt class="py-lineno"> 352</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">lit</tt> <tt class="py-keyword">in</tt> <tt id="link-61" class="py-name"><a title="spade.logic.literals" class="py-name" href="#" onclick="return doclink('link-61', 'literals', 'link-57');">literals</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L353"></a><tt class="py-lineno"> 353</tt>  <tt class="py-line">            <tt class="py-name">vars</tt> <tt class="py-op">=</tt> <tt class="py-name">vars</tt><tt class="py-op">.</tt><tt class="py-name">union</tt><tt class="py-op">(</tt><tt id="link-62" class="py-name" targets="Function spade.logic.variables()=spade.logic-module.html#variables"><a title="spade.logic.variables" class="py-name" href="#" onclick="return doclink('link-62', 'variables', 'link-62');">variables</a></tt><tt class="py-op">(</tt><tt class="py-name">lit</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L354"></a><tt class="py-lineno"> 354</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">vars</tt> </tt>
</div><a name="L355"></a><tt class="py-lineno"> 355</tt>  <tt class="py-line">     </tt>
<a name="is_definite_clause"></a><div id="is_definite_clause-def"><a name="L356"></a><tt class="py-lineno"> 356</tt> <a class="py-toggle" href="#" id="is_definite_clause-toggle" onclick="return toggle('is_definite_clause');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_definite_clause">is_definite_clause</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_definite_clause-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_definite_clause-expanded"><a name="L357"></a><tt class="py-lineno"> 357</tt>  <tt class="py-line">    <tt class="py-docstring">"""returns True for exprs s of the form A &amp; B &amp; ... &amp; C ==&gt; D,</tt> </tt>
<a name="L358"></a><tt class="py-lineno"> 358</tt>  <tt class="py-line"><tt class="py-docstring">    where all literals are positive.  In clause form, this is</tt> </tt>
<a name="L359"></a><tt class="py-lineno"> 359</tt>  <tt class="py-line"><tt class="py-docstring">    ~A | ~B | ... | ~C | D, where exactly one clause is positive.</tt> </tt>
<a name="L360"></a><tt class="py-lineno"> 360</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_definite_clause(expr('Farmer(Mac)'))</tt> </tt>
<a name="L361"></a><tt class="py-lineno"> 361</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L362"></a><tt class="py-lineno"> 362</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_definite_clause(expr('~Farmer(Mac)'))</tt> </tt>
<a name="L363"></a><tt class="py-lineno"> 363</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L364"></a><tt class="py-lineno"> 364</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_definite_clause(expr('(Farmer(f) &amp; Rabbit(r)) ==&gt; Hates(f, r)'))</tt> </tt>
<a name="L365"></a><tt class="py-lineno"> 365</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L366"></a><tt class="py-lineno"> 366</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_definite_clause(expr('(Farmer(f) &amp; ~Rabbit(r)) ==&gt; Hates(f, r)'))</tt> </tt>
<a name="L367"></a><tt class="py-lineno"> 367</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L368"></a><tt class="py-lineno"> 368</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L369"></a><tt class="py-lineno"> 369</tt>  <tt class="py-line">    <tt class="py-name">op</tt> <tt class="py-op">=</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> </tt>
<a name="L370"></a><tt class="py-lineno"> 370</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-63" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-63', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> </tt>
<a name="L371"></a><tt class="py-lineno"> 371</tt>  <tt class="py-line">            <tt class="py-op">(</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt> <tt class="py-keyword">and</tt> <tt id="link-64" class="py-name" targets="Function spade.logic.every()=spade.logic-module.html#every"><a title="spade.logic.every" class="py-name" href="#" onclick="return doclink('link-64', 'every', 'link-64');">every</a></tt><tt class="py-op">(</tt><tt id="link-65" class="py-name" targets="Function spade.logic.is_positive()=spade.logic-module.html#is_positive"><a title="spade.logic.is_positive" class="py-name" href="#" onclick="return doclink('link-65', 'is_positive', 'link-65');">is_positive</a></tt><tt class="py-op">,</tt> <tt id="link-66" class="py-name"><a title="spade.logic.literals" class="py-name" href="#" onclick="return doclink('link-66', 'literals', 'link-57');">literals</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L372"></a><tt class="py-lineno"> 372</tt>  <tt class="py-line"> </tt>
<a name="L373"></a><tt class="py-lineno"> 373</tt>  <tt class="py-line"><tt class="py-comment">## Useful constant Exprs used in examples and code:</tt> </tt>
<a name="L374"></a><tt class="py-lineno"> 374</tt>  <tt class="py-line"><tt id="link-67" class="py-name" targets="Variable spade.bdi.TRUE=spade.bdi-module.html#TRUE,Variable spade.logic.TRUE=spade.logic-module.html#TRUE"><a title="spade.bdi.TRUE
spade.logic.TRUE" class="py-name" href="#" onclick="return doclink('link-67', 'TRUE', 'link-67');">TRUE</a></tt><tt class="py-op">,</tt> <tt id="link-68" class="py-name" targets="Variable spade.bdi.FALSE=spade.bdi-module.html#FALSE,Variable spade.logic.FALSE=spade.logic-module.html#FALSE"><a title="spade.bdi.FALSE
spade.logic.FALSE" class="py-name" href="#" onclick="return doclink('link-68', 'FALSE', 'link-68');">FALSE</a></tt><tt class="py-op">,</tt> <tt id="link-69" class="py-name" targets="Variable spade.bdi.ZERO=spade.bdi-module.html#ZERO,Variable spade.logic.ZERO=spade.logic-module.html#ZERO"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-69', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">,</tt> <tt id="link-70" class="py-name" targets="Variable spade.bdi.ONE=spade.bdi-module.html#ONE,Variable spade.logic.ONE=spade.logic-module.html#ONE"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-70', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">,</tt> <tt id="link-71" class="py-name" targets="Variable spade.bdi.TWO=spade.bdi-module.html#TWO,Variable spade.logic.TWO=spade.logic-module.html#TWO"><a title="spade.bdi.TWO
spade.logic.TWO" class="py-name" href="#" onclick="return doclink('link-71', 'TWO', 'link-71');">TWO</a></tt> <tt class="py-op">=</tt> <tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-72" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-72', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">,</tt> <tt class="py-op">[</tt><tt class="py-string">'TRUE'</tt><tt class="py-op">,</tt> <tt class="py-string">'FALSE'</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-number">2</tt><tt class="py-op">]</tt><tt class="py-op">)</tt>  </tt>
<a name="L375"></a><tt class="py-lineno"> 375</tt>  <tt class="py-line"><tt id="link-73" class="py-name" targets="Variable spade.bdi.A=spade.bdi-module.html#A,Variable spade.logic.A=spade.logic-module.html#A"><a title="spade.bdi.A
spade.logic.A" class="py-name" href="#" onclick="return doclink('link-73', 'A', 'link-73');">A</a></tt><tt class="py-op">,</tt> <tt id="link-74" class="py-name" targets="Variable spade.bdi.B=spade.bdi-module.html#B,Variable spade.logic.B=spade.logic-module.html#B"><a title="spade.bdi.B
spade.logic.B" class="py-name" href="#" onclick="return doclink('link-74', 'B', 'link-74');">B</a></tt><tt class="py-op">,</tt> <tt id="link-75" class="py-name" targets="Variable spade.bdi.C=spade.bdi-module.html#C,Variable spade.logic.C=spade.logic-module.html#C,Function spade.xmpp.auth.C()=spade.xmpp.auth-module.html#C,Function spade.xmppd.modules.stream.C()=spade.xmppd.modules.stream-module.html#C"><a title="spade.bdi.C
spade.logic.C
spade.xmpp.auth.C
spade.xmppd.modules.stream.C" class="py-name" href="#" onclick="return doclink('link-75', 'C', 'link-75');">C</a></tt><tt class="py-op">,</tt> <tt id="link-76" class="py-name" targets="Variable spade.bdi.F=spade.bdi-module.html#F,Variable spade.logic.F=spade.logic-module.html#F"><a title="spade.bdi.F
spade.logic.F" class="py-name" href="#" onclick="return doclink('link-76', 'F', 'link-76');">F</a></tt><tt class="py-op">,</tt> <tt id="link-77" class="py-name" targets="Variable spade.bdi.G=spade.bdi-module.html#G,Variable spade.logic.G=spade.logic-module.html#G"><a title="spade.bdi.G
spade.logic.G" class="py-name" href="#" onclick="return doclink('link-77', 'G', 'link-77');">G</a></tt><tt class="py-op">,</tt> <tt id="link-78" class="py-name" targets="Variable spade.bdi.P=spade.bdi-module.html#P,Variable spade.logic.P=spade.logic-module.html#P"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-78', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt id="link-79" class="py-name" targets="Variable spade.bdi.Q=spade.bdi-module.html#Q,Variable spade.logic.Q=spade.logic-module.html#Q"><a title="spade.bdi.Q
spade.logic.Q" class="py-name" href="#" onclick="return doclink('link-79', 'Q', 'link-79');">Q</a></tt><tt class="py-op">,</tt> <tt id="link-80" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-80', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-81" class="py-name" targets="Variable spade.bdi.y=spade.bdi-module.html#y,Variable spade.logic.y=spade.logic-module.html#y"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-81', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt id="link-82" class="py-name" targets="Variable spade.bdi.z=spade.bdi-module.html#z,Variable spade.logic.z=spade.logic-module.html#z"><a title="spade.bdi.z
spade.logic.z" class="py-name" href="#" onclick="return doclink('link-82', 'z', 'link-82');">z</a></tt>  <tt class="py-op">=</tt> <tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-83" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-83', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">,</tt> <tt class="py-string">'ABCFGPQxyz'</tt><tt class="py-op">)</tt>  </tt>
<a name="L376"></a><tt class="py-lineno"> 376</tt>  <tt class="py-line"> </tt>
<a name="L377"></a><tt class="py-lineno"> 377</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L378"></a><tt class="py-lineno"> 378</tt>  <tt class="py-line"> </tt>
<a name="tt_entails"></a><div id="tt_entails-def"><a name="L379"></a><tt class="py-lineno"> 379</tt> <a class="py-toggle" href="#" id="tt_entails-toggle" onclick="return toggle('tt_entails');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#tt_entails">tt_entails</a><tt class="py-op">(</tt><tt class="py-param">kb</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="tt_entails-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="tt_entails-expanded"><a name="L380"></a><tt class="py-lineno"> 380</tt>  <tt class="py-line">    <tt class="py-docstring">"""Use truth tables to determine if KB entails sentence alpha. [Fig. 7.10]</tt> </tt>
<a name="L381"></a><tt class="py-lineno"> 381</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; tt_entails(expr('P &amp; Q'), expr('Q'))</tt> </tt>
<a name="L382"></a><tt class="py-lineno"> 382</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L383"></a><tt class="py-lineno"> 383</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L384"></a><tt class="py-lineno"> 384</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-84" class="py-name" targets="Function spade.logic.tt_check_all()=spade.logic-module.html#tt_check_all"><a title="spade.logic.tt_check_all" class="py-name" href="#" onclick="return doclink('link-84', 'tt_check_all', 'link-84');">tt_check_all</a></tt><tt class="py-op">(</tt><tt class="py-name">kb</tt><tt class="py-op">,</tt> <tt class="py-name">alpha</tt><tt class="py-op">,</tt> <tt id="link-85" class="py-name" targets="Function spade.logic.prop_symbols()=spade.logic-module.html#prop_symbols"><a title="spade.logic.prop_symbols" class="py-name" href="#" onclick="return doclink('link-85', 'prop_symbols', 'link-85');">prop_symbols</a></tt><tt class="py-op">(</tt><tt class="py-name">kb</tt> <tt class="py-op">&amp;</tt> <tt class="py-name">alpha</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">)</tt> </tt>
</div><a name="L385"></a><tt class="py-lineno"> 385</tt>  <tt class="py-line"> </tt>
<a name="tt_check_all"></a><div id="tt_check_all-def"><a name="L386"></a><tt class="py-lineno"> 386</tt> <a class="py-toggle" href="#" id="tt_check_all-toggle" onclick="return toggle('tt_check_all');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#tt_check_all">tt_check_all</a><tt class="py-op">(</tt><tt class="py-param">kb</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">,</tt> <tt class="py-param">symbols</tt><tt class="py-op">,</tt> <tt class="py-param">model</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="tt_check_all-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="tt_check_all-expanded"><a name="L387"></a><tt class="py-lineno"> 387</tt>  <tt class="py-line">    <tt class="py-docstring">"Auxiliary routine to implement tt_entails."</tt> </tt>
<a name="L388"></a><tt class="py-lineno"> 388</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">symbols</tt><tt class="py-op">:</tt> </tt>
<a name="L389"></a><tt class="py-lineno"> 389</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt id="link-86" class="py-name" targets="Function spade.logic.pl_true()=spade.logic-module.html#pl_true"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-86', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">kb</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-87" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-87', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">alpha</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L390"></a><tt class="py-lineno"> 390</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L391"></a><tt class="py-lineno"> 391</tt>  <tt class="py-line">        <tt class="py-keyword">assert</tt> <tt class="py-name">result</tt> <tt class="py-op">!=</tt> <tt class="py-name">None</tt> </tt>
<a name="L392"></a><tt class="py-lineno"> 392</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L393"></a><tt class="py-lineno"> 393</tt>  <tt class="py-line">        <tt id="link-88" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-88', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">rest</tt> <tt class="py-op">=</tt> <tt class="py-name">symbols</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">symbols</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L394"></a><tt class="py-lineno"> 394</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-89" class="py-name"><a title="spade.logic.tt_check_all" class="py-name" href="#" onclick="return doclink('link-89', 'tt_check_all', 'link-84');">tt_check_all</a></tt><tt class="py-op">(</tt><tt class="py-name">kb</tt><tt class="py-op">,</tt> <tt class="py-name">alpha</tt><tt class="py-op">,</tt> <tt class="py-name">rest</tt><tt class="py-op">,</tt> <tt id="link-90" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-90', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt id="link-91" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-91', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">True</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> </tt>
<a name="L395"></a><tt class="py-lineno"> 395</tt>  <tt class="py-line">                <tt id="link-92" class="py-name"><a title="spade.logic.tt_check_all" class="py-name" href="#" onclick="return doclink('link-92', 'tt_check_all', 'link-84');">tt_check_all</a></tt><tt class="py-op">(</tt><tt class="py-name">kb</tt><tt class="py-op">,</tt> <tt class="py-name">alpha</tt><tt class="py-op">,</tt> <tt class="py-name">rest</tt><tt class="py-op">,</tt> <tt id="link-93" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-93', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt id="link-94" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-94', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L396"></a><tt class="py-lineno"> 396</tt>  <tt class="py-line"> </tt>
<a name="prop_symbols"></a><div id="prop_symbols-def"><a name="L397"></a><tt class="py-lineno"> 397</tt> <a class="py-toggle" href="#" id="prop_symbols-toggle" onclick="return toggle('prop_symbols');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#prop_symbols">prop_symbols</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="prop_symbols-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="prop_symbols-expanded"><a name="L398"></a><tt class="py-lineno"> 398</tt>  <tt class="py-line">    <tt class="py-docstring">"Return a list of all propositional symbols in x."</tt> </tt>
<a name="L399"></a><tt class="py-lineno"> 399</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-95" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-95', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-96" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-96', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L400"></a><tt class="py-lineno"> 400</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L401"></a><tt class="py-lineno"> 401</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-97" class="py-name" targets="Function spade.logic.is_prop_symbol()=spade.logic-module.html#is_prop_symbol"><a title="spade.logic.is_prop_symbol" class="py-name" href="#" onclick="return doclink('link-97', 'is_prop_symbol', 'link-97');">is_prop_symbol</a></tt><tt class="py-op">(</tt><tt id="link-98" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-98', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L402"></a><tt class="py-lineno"> 402</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt id="link-99" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-99', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt> </tt>
<a name="L403"></a><tt class="py-lineno"> 403</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L404"></a><tt class="py-lineno"> 404</tt>  <tt class="py-line">        <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L405"></a><tt class="py-lineno"> 405</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">arg</tt> <tt class="py-keyword">in</tt> <tt id="link-100" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-100', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">:</tt> </tt>
<a name="L406"></a><tt class="py-lineno"> 406</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt class="py-name">symbol</tt> <tt class="py-keyword">in</tt> <tt id="link-101" class="py-name"><a title="spade.logic.prop_symbols" class="py-name" href="#" onclick="return doclink('link-101', 'prop_symbols', 'link-85');">prop_symbols</a></tt><tt class="py-op">(</tt><tt class="py-name">arg</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L407"></a><tt class="py-lineno"> 407</tt>  <tt class="py-line">                <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">add</tt><tt class="py-op">(</tt><tt class="py-name">symbol</tt><tt class="py-op">)</tt> </tt>
<a name="L408"></a><tt class="py-lineno"> 408</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">list</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
</div><a name="L409"></a><tt class="py-lineno"> 409</tt>  <tt class="py-line"> </tt>
<a name="tt_true"></a><div id="tt_true-def"><a name="L410"></a><tt class="py-lineno"> 410</tt> <a class="py-toggle" href="#" id="tt_true-toggle" onclick="return toggle('tt_true');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#tt_true">tt_true</a><tt class="py-op">(</tt><tt class="py-param">alpha</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="tt_true-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="tt_true-expanded"><a name="L411"></a><tt class="py-lineno"> 411</tt>  <tt class="py-line">    <tt class="py-docstring">"""Is the sentence alpha a tautology? (alpha will be coerced to an expr.)</tt> </tt>
<a name="L412"></a><tt class="py-lineno"> 412</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; tt_true(expr("(P &gt;&gt; Q) &lt;=&gt; (~P | Q)"))</tt> </tt>
<a name="L413"></a><tt class="py-lineno"> 413</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L414"></a><tt class="py-lineno"> 414</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L415"></a><tt class="py-lineno"> 415</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-102" class="py-name"><a title="spade.logic.tt_entails" class="py-name" href="#" onclick="return doclink('link-102', 'tt_entails', 'link-15');">tt_entails</a></tt><tt class="py-op">(</tt><tt id="link-103" class="py-name"><a title="spade.bdi.TRUE
spade.logic.TRUE" class="py-name" href="#" onclick="return doclink('link-103', 'TRUE', 'link-67');">TRUE</a></tt><tt class="py-op">,</tt> <tt id="link-104" class="py-name"><a title="spade.logic.expr" class="py-name" href="#" onclick="return doclink('link-104', 'expr', 'link-24');">expr</a></tt><tt class="py-op">(</tt><tt class="py-name">alpha</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L416"></a><tt class="py-lineno"> 416</tt>  <tt class="py-line"> </tt>
<a name="pl_true"></a><div id="pl_true-def"><a name="L417"></a><tt class="py-lineno"> 417</tt> <a class="py-toggle" href="#" id="pl_true-toggle" onclick="return toggle('pl_true');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pl_true">pl_true</a><tt class="py-op">(</tt><tt class="py-param">exp</tt><tt class="py-op">,</tt> <tt class="py-param">model</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pl_true-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pl_true-expanded"><a name="L418"></a><tt class="py-lineno"> 418</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return True if the propositional logic expression is true in the model,</tt> </tt>
<a name="L419"></a><tt class="py-lineno"> 419</tt>  <tt class="py-line"><tt class="py-docstring">    and False if it is false. If the model does not specify the value for</tt> </tt>
<a name="L420"></a><tt class="py-lineno"> 420</tt>  <tt class="py-line"><tt class="py-docstring">    every proposition, this may return None to indicate 'not obvious';</tt> </tt>
<a name="L421"></a><tt class="py-lineno"> 421</tt>  <tt class="py-line"><tt class="py-docstring">    this may happen even when the expression is tautological."""</tt> </tt>
<a name="L422"></a><tt class="py-lineno"> 422</tt>  <tt class="py-line">    <tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">exp</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">exp</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> </tt>
<a name="L423"></a><tt class="py-lineno"> 423</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">exp</tt> <tt class="py-op">==</tt> <tt id="link-105" class="py-name"><a title="spade.bdi.TRUE
spade.logic.TRUE" class="py-name" href="#" onclick="return doclink('link-105', 'TRUE', 'link-67');">TRUE</a></tt><tt class="py-op">:</tt> </tt>
<a name="L424"></a><tt class="py-lineno"> 424</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L425"></a><tt class="py-lineno"> 425</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">exp</tt> <tt class="py-op">==</tt> <tt id="link-106" class="py-name"><a title="spade.bdi.FALSE
spade.logic.FALSE" class="py-name" href="#" onclick="return doclink('link-106', 'FALSE', 'link-68');">FALSE</a></tt><tt class="py-op">:</tt> </tt>
<a name="L426"></a><tt class="py-lineno"> 426</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
<a name="L427"></a><tt class="py-lineno"> 427</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-107" class="py-name"><a title="spade.logic.is_prop_symbol" class="py-name" href="#" onclick="return doclink('link-107', 'is_prop_symbol', 'link-97');">is_prop_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L428"></a><tt class="py-lineno"> 428</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">model</tt><tt class="py-op">.</tt><tt id="link-108" class="py-name" targets="Method spade.xmppd.modules.db_fake.DB.get()=spade.xmppd.modules.db_fake.DB-class.html#get"><a title="spade.xmppd.modules.db_fake.DB.get" class="py-name" href="#" onclick="return doclink('link-108', 'get', 'link-108');">get</a></tt><tt class="py-op">(</tt><tt class="py-name">exp</tt><tt class="py-op">)</tt> </tt>
<a name="L429"></a><tt class="py-lineno"> 429</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'~'</tt><tt class="py-op">:</tt> </tt>
<a name="L430"></a><tt class="py-lineno"> 430</tt>  <tt class="py-line">        <tt class="py-name">p</tt> <tt class="py-op">=</tt> <tt id="link-109" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-109', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L431"></a><tt class="py-lineno"> 431</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">p</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
<a name="L432"></a><tt class="py-lineno"> 432</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-keyword">not</tt> <tt class="py-name">p</tt> </tt>
<a name="L433"></a><tt class="py-lineno"> 433</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'|'</tt><tt class="py-op">:</tt> </tt>
<a name="L434"></a><tt class="py-lineno"> 434</tt>  <tt class="py-line">        <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt> </tt>
<a name="L435"></a><tt class="py-lineno"> 435</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">arg</tt> <tt class="py-keyword">in</tt> <tt class="py-name">args</tt><tt class="py-op">:</tt> </tt>
<a name="L436"></a><tt class="py-lineno"> 436</tt>  <tt class="py-line">            <tt class="py-name">p</tt> <tt class="py-op">=</tt> <tt id="link-110" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-110', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">arg</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L437"></a><tt class="py-lineno"> 437</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">p</tt> <tt class="py-op">==</tt> <tt class="py-name">True</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L438"></a><tt class="py-lineno"> 438</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">p</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L439"></a><tt class="py-lineno"> 439</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">result</tt> </tt>
<a name="L440"></a><tt class="py-lineno"> 440</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&amp;'</tt><tt class="py-op">:</tt> </tt>
<a name="L441"></a><tt class="py-lineno"> 441</tt>  <tt class="py-line">        <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt class="py-name">True</tt> </tt>
<a name="L442"></a><tt class="py-lineno"> 442</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">arg</tt> <tt class="py-keyword">in</tt> <tt class="py-name">args</tt><tt class="py-op">:</tt> </tt>
<a name="L443"></a><tt class="py-lineno"> 443</tt>  <tt class="py-line">            <tt class="py-name">p</tt> <tt class="py-op">=</tt> <tt id="link-111" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-111', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">arg</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L444"></a><tt class="py-lineno"> 444</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">p</tt> <tt class="py-op">==</tt> <tt class="py-name">False</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
<a name="L445"></a><tt class="py-lineno"> 445</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">p</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> <tt class="py-name">result</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L446"></a><tt class="py-lineno"> 446</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">result</tt> </tt>
<a name="L447"></a><tt class="py-lineno"> 447</tt>  <tt class="py-line">    <tt class="py-name">p</tt><tt class="py-op">,</tt> <tt class="py-name">q</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt> </tt>
<a name="L448"></a><tt class="py-lineno"> 448</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">:</tt> </tt>
<a name="L449"></a><tt class="py-lineno"> 449</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-112" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-112', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-op">~</tt><tt class="py-name">p</tt> <tt class="py-op">|</tt> <tt class="py-name">q</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L450"></a><tt class="py-lineno"> 450</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&lt;&lt;'</tt><tt class="py-op">:</tt> </tt>
<a name="L451"></a><tt class="py-lineno"> 451</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-113" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-113', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">p</tt> <tt class="py-op">|</tt> <tt class="py-op">~</tt><tt class="py-name">q</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L452"></a><tt class="py-lineno"> 452</tt>  <tt class="py-line">    <tt class="py-name">pt</tt> <tt class="py-op">=</tt> <tt id="link-114" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-114', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">p</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L453"></a><tt class="py-lineno"> 453</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">pt</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
<a name="L454"></a><tt class="py-lineno"> 454</tt>  <tt class="py-line">    <tt class="py-name">qt</tt> <tt class="py-op">=</tt> <tt id="link-115" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-115', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">q</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L455"></a><tt class="py-lineno"> 455</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">qt</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
<a name="L456"></a><tt class="py-lineno"> 456</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&lt;=&gt;'</tt><tt class="py-op">:</tt> </tt>
<a name="L457"></a><tt class="py-lineno"> 457</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">pt</tt> <tt class="py-op">==</tt> <tt class="py-name">qt</tt> </tt>
<a name="L458"></a><tt class="py-lineno"> 458</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'^'</tt><tt class="py-op">:</tt> </tt>
<a name="L459"></a><tt class="py-lineno"> 459</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">pt</tt> <tt class="py-op">!=</tt> <tt class="py-name">qt</tt> </tt>
<a name="L460"></a><tt class="py-lineno"> 460</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L461"></a><tt class="py-lineno"> 461</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">,</tt> <tt class="py-string">"illegal operator in logic expression"</tt> <tt class="py-op">+</tt> <tt class="py-name">str</tt><tt class="py-op">(</tt><tt class="py-name">exp</tt><tt class="py-op">)</tt> </tt>
</div><a name="L462"></a><tt class="py-lineno"> 462</tt>  <tt class="py-line"> </tt>
<a name="L463"></a><tt class="py-lineno"> 463</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L464"></a><tt class="py-lineno"> 464</tt>  <tt class="py-line"> </tt>
<a name="L465"></a><tt class="py-lineno"> 465</tt>  <tt class="py-line"><tt class="py-comment">## Convert to Conjunctive Normal Form (CNF)</tt> </tt>
<a name="L466"></a><tt class="py-lineno"> 466</tt>  <tt class="py-line">  </tt>
<a name="to_cnf"></a><div id="to_cnf-def"><a name="L467"></a><tt class="py-lineno"> 467</tt> <a class="py-toggle" href="#" id="to_cnf-toggle" onclick="return toggle('to_cnf');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#to_cnf">to_cnf</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="to_cnf-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="to_cnf-expanded"><a name="L468"></a><tt class="py-lineno"> 468</tt>  <tt class="py-line">    <tt class="py-docstring">"""Convert a propositional logical sentence s to conjunctive normal form.</tt> </tt>
<a name="L469"></a><tt class="py-lineno"> 469</tt>  <tt class="py-line"><tt class="py-docstring">    That is, of the form ((A | ~B | ...) &amp; (B | C | ...) &amp; ...) [p. 215]</tt> </tt>
<a name="L470"></a><tt class="py-lineno"> 470</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; to_cnf("~(B|C)")</tt> </tt>
<a name="L471"></a><tt class="py-lineno"> 471</tt>  <tt class="py-line"><tt class="py-docstring">    (~B &amp; ~C)</tt> </tt>
<a name="L472"></a><tt class="py-lineno"> 472</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; to_cnf("B &lt;=&gt; (P1|P2)")</tt> </tt>
<a name="L473"></a><tt class="py-lineno"> 473</tt>  <tt class="py-line"><tt class="py-docstring">    ((~P1 | B) &amp; (~P2 | B) &amp; (P1 | P2 | ~B))</tt> </tt>
<a name="L474"></a><tt class="py-lineno"> 474</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; to_cnf("a | (b &amp; c) | d")</tt> </tt>
<a name="L475"></a><tt class="py-lineno"> 475</tt>  <tt class="py-line"><tt class="py-docstring">    ((b | a | d) &amp; (c | a | d))</tt> </tt>
<a name="L476"></a><tt class="py-lineno"> 476</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; to_cnf("A &amp; (B | (D &amp; E))")</tt> </tt>
<a name="L477"></a><tt class="py-lineno"> 477</tt>  <tt class="py-line"><tt class="py-docstring">    (A &amp; (D | B) &amp; (E | B))</tt> </tt>
<a name="L478"></a><tt class="py-lineno"> 478</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L479"></a><tt class="py-lineno"> 479</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">str</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt id="link-116" class="py-name"><a title="spade.logic.expr" class="py-name" href="#" onclick="return doclink('link-116', 'expr', 'link-24');">expr</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L480"></a><tt class="py-lineno"> 480</tt>  <tt class="py-line">    <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt id="link-117" class="py-name" targets="Function spade.logic.eliminate_implications()=spade.logic-module.html#eliminate_implications"><a title="spade.logic.eliminate_implications" class="py-name" href="#" onclick="return doclink('link-117', 'eliminate_implications', 'link-117');">eliminate_implications</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-comment"># Steps 1, 2 from p. 215</tt> </tt>
<a name="L481"></a><tt class="py-lineno"> 481</tt>  <tt class="py-line">    <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt id="link-118" class="py-name" targets="Function spade.logic.move_not_inwards()=spade.logic-module.html#move_not_inwards"><a title="spade.logic.move_not_inwards" class="py-name" href="#" onclick="return doclink('link-118', 'move_not_inwards', 'link-118');">move_not_inwards</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-comment"># Step 3</tt> </tt>
<a name="L482"></a><tt class="py-lineno"> 482</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-119" class="py-name" targets="Function spade.logic.distribute_and_over_or()=spade.logic-module.html#distribute_and_over_or"><a title="spade.logic.distribute_and_over_or" class="py-name" href="#" onclick="return doclink('link-119', 'distribute_and_over_or', 'link-119');">distribute_and_over_or</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-comment"># Step 4</tt> </tt>
</div><a name="L483"></a><tt class="py-lineno"> 483</tt>  <tt class="py-line">     </tt>
<a name="eliminate_implications"></a><div id="eliminate_implications-def"><a name="L484"></a><tt class="py-lineno"> 484</tt> <a class="py-toggle" href="#" id="eliminate_implications-toggle" onclick="return toggle('eliminate_implications');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#eliminate_implications">eliminate_implications</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="eliminate_implications-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="eliminate_implications-expanded"><a name="L485"></a><tt class="py-lineno"> 485</tt>  <tt class="py-line">    <tt class="py-docstring">"""Change &gt;&gt;, &lt;&lt;, and &lt;=&gt; into &amp;, |, and ~. That is, return an Expr</tt> </tt>
<a name="L486"></a><tt class="py-lineno"> 486</tt>  <tt class="py-line"><tt class="py-docstring">    that is equivalent to s, but has only &amp;, |, and ~ as logical operators.</tt> </tt>
<a name="L487"></a><tt class="py-lineno"> 487</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; eliminate_implications(A &gt;&gt; (~B &lt;&lt; C))</tt> </tt>
<a name="L488"></a><tt class="py-lineno"> 488</tt>  <tt class="py-line"><tt class="py-docstring">    ((~B | ~C) | ~A)</tt> </tt>
<a name="L489"></a><tt class="py-lineno"> 489</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L490"></a><tt class="py-lineno"> 490</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> <tt class="py-keyword">or</tt> <tt id="link-120" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-120', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">s</tt>     <tt class="py-comment">## (Atoms are unchanged.)</tt> </tt>
<a name="L491"></a><tt class="py-lineno"> 491</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-121" class="py-name"><a title="spade.logic.eliminate_implications" class="py-name" href="#" onclick="return doclink('link-121', 'eliminate_implications', 'link-117');">eliminate_implications</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L492"></a><tt class="py-lineno"> 492</tt>  <tt class="py-line">    <tt id="link-122" class="py-name" targets="Variable spade.ACLMessage.ACLMessage.a=spade.ACLMessage.ACLMessage-class.html#a"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-122', 'a', 'link-122');">a</a></tt><tt class="py-op">,</tt> <tt class="py-name">b</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L493"></a><tt class="py-lineno"> 493</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">:</tt> </tt>
<a name="L494"></a><tt class="py-lineno"> 494</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-name">b</tt> <tt class="py-op">|</tt> <tt class="py-op">~</tt><tt id="link-123" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-123', 'a', 'link-122');">a</a></tt><tt class="py-op">)</tt> </tt>
<a name="L495"></a><tt class="py-lineno"> 495</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&lt;&lt;'</tt><tt class="py-op">:</tt> </tt>
<a name="L496"></a><tt class="py-lineno"> 496</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-124" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-124', 'a', 'link-122');">a</a></tt> <tt class="py-op">|</tt> <tt class="py-op">~</tt><tt class="py-name">b</tt><tt class="py-op">)</tt> </tt>
<a name="L497"></a><tt class="py-lineno"> 497</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&lt;=&gt;'</tt><tt class="py-op">:</tt> </tt>
<a name="L498"></a><tt class="py-lineno"> 498</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-125" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-125', 'a', 'link-122');">a</a></tt> <tt class="py-op">|</tt> <tt class="py-op">~</tt><tt class="py-name">b</tt><tt class="py-op">)</tt> <tt class="py-op">&amp;</tt> <tt class="py-op">(</tt><tt class="py-name">b</tt> <tt class="py-op">|</tt> <tt class="py-op">~</tt><tt id="link-126" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-126', 'a', 'link-122');">a</a></tt><tt class="py-op">)</tt> </tt>
<a name="L499"></a><tt class="py-lineno"> 499</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L500"></a><tt class="py-lineno"> 500</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-127" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-127', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
</div><a name="L501"></a><tt class="py-lineno"> 501</tt>  <tt class="py-line"> </tt>
<a name="move_not_inwards"></a><div id="move_not_inwards-def"><a name="L502"></a><tt class="py-lineno"> 502</tt> <a class="py-toggle" href="#" id="move_not_inwards-toggle" onclick="return toggle('move_not_inwards');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#move_not_inwards">move_not_inwards</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="move_not_inwards-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="move_not_inwards-expanded"><a name="L503"></a><tt class="py-lineno"> 503</tt>  <tt class="py-line">    <tt class="py-docstring">"""Rewrite sentence s by moving negation sign inward.</tt> </tt>
<a name="L504"></a><tt class="py-lineno"> 504</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; move_not_inwards(~(A | B))</tt> </tt>
<a name="L505"></a><tt class="py-lineno"> 505</tt>  <tt class="py-line"><tt class="py-docstring">    (~A &amp; ~B)</tt> </tt>
<a name="L506"></a><tt class="py-lineno"> 506</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; move_not_inwards(~(A &amp; B))</tt> </tt>
<a name="L507"></a><tt class="py-lineno"> 507</tt>  <tt class="py-line"><tt class="py-docstring">    (~A | ~B)</tt> </tt>
<a name="L508"></a><tt class="py-lineno"> 508</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; move_not_inwards(~(~(A | ~B) | ~~C))</tt> </tt>
<a name="L509"></a><tt class="py-lineno"> 509</tt>  <tt class="py-line"><tt class="py-docstring">    ((A | ~B) &amp; ~C)</tt> </tt>
<a name="L510"></a><tt class="py-lineno"> 510</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L511"></a><tt class="py-lineno"> 511</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'~'</tt><tt class="py-op">:</tt> </tt>
<a name="L512"></a><tt class="py-lineno"> 512</tt>  <tt class="py-line">        <tt class="py-name">NOT</tt> <tt class="py-op">=</tt> <tt class="py-keyword">lambda</tt> <tt class="py-name">b</tt><tt class="py-op">:</tt> <tt id="link-128" class="py-name"><a title="spade.logic.move_not_inwards" class="py-name" href="#" onclick="return doclink('link-128', 'move_not_inwards', 'link-118');">move_not_inwards</a></tt><tt class="py-op">(</tt><tt class="py-op">~</tt><tt class="py-name">b</tt><tt class="py-op">)</tt> </tt>
<a name="L513"></a><tt class="py-lineno"> 513</tt>  <tt class="py-line">        <tt id="link-129" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-129', 'a', 'link-122');">a</a></tt> <tt class="py-op">=</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L514"></a><tt class="py-lineno"> 514</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt id="link-130" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-130', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'~'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-131" class="py-name"><a title="spade.logic.move_not_inwards" class="py-name" href="#" onclick="return doclink('link-131', 'move_not_inwards', 'link-118');">move_not_inwards</a></tt><tt class="py-op">(</tt><tt id="link-132" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-132', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-comment"># ~~A ==&gt; A</tt> </tt>
<a name="L515"></a><tt class="py-lineno"> 515</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt id="link-133" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-133', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-134" class="py-name" targets="Function spade.logic.NaryExpr()=spade.logic-module.html#NaryExpr"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-134', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'|'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt class="py-name">NOT</tt><tt class="py-op">,</tt> <tt id="link-135" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-135', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L516"></a><tt class="py-lineno"> 516</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt id="link-136" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-136', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt><tt class="py-string">'|'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-137" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-137', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt class="py-name">NOT</tt><tt class="py-op">,</tt> <tt id="link-138" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-138', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L517"></a><tt class="py-lineno"> 517</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt> </tt>
<a name="L518"></a><tt class="py-lineno"> 518</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-139" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-139', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-keyword">not</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">:</tt> </tt>
<a name="L519"></a><tt class="py-lineno"> 519</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt> </tt>
<a name="L520"></a><tt class="py-lineno"> 520</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L521"></a><tt class="py-lineno"> 521</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-140" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-140', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-141" class="py-name"><a title="spade.logic.move_not_inwards" class="py-name" href="#" onclick="return doclink('link-141', 'move_not_inwards', 'link-118');">move_not_inwards</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L522"></a><tt class="py-lineno"> 522</tt>  <tt class="py-line"> </tt>
<a name="distribute_and_over_or"></a><div id="distribute_and_over_or-def"><a name="L523"></a><tt class="py-lineno"> 523</tt> <a class="py-toggle" href="#" id="distribute_and_over_or-toggle" onclick="return toggle('distribute_and_over_or');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#distribute_and_over_or">distribute_and_over_or</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="distribute_and_over_or-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="distribute_and_over_or-expanded"><a name="L524"></a><tt class="py-lineno"> 524</tt>  <tt class="py-line">    <tt class="py-docstring">"""Given a sentence s consisting of conjunctions and disjunctions</tt> </tt>
<a name="L525"></a><tt class="py-lineno"> 525</tt>  <tt class="py-line"><tt class="py-docstring">    of literals, return an equivalent sentence in CNF.</tt> </tt>
<a name="L526"></a><tt class="py-lineno"> 526</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; distribute_and_over_or((A &amp; B) | C)</tt> </tt>
<a name="L527"></a><tt class="py-lineno"> 527</tt>  <tt class="py-line"><tt class="py-docstring">    ((A | C) &amp; (B | C))</tt> </tt>
<a name="L528"></a><tt class="py-lineno"> 528</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L529"></a><tt class="py-lineno"> 529</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'|'</tt><tt class="py-op">:</tt> </tt>
<a name="L530"></a><tt class="py-lineno"> 530</tt>  <tt class="py-line">        <tt class="py-name">s</tt> <tt class="py-op">=</tt> <tt id="link-142" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-142', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'|'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L531"></a><tt class="py-lineno"> 531</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt>  </tt>
<a name="L532"></a><tt class="py-lineno"> 532</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt id="link-143" class="py-name"><a title="spade.bdi.FALSE
spade.logic.FALSE" class="py-name" href="#" onclick="return doclink('link-143', 'FALSE', 'link-68');">FALSE</a></tt> </tt>
<a name="L533"></a><tt class="py-lineno"> 533</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt>  </tt>
<a name="L534"></a><tt class="py-lineno"> 534</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt id="link-144" class="py-name"><a title="spade.logic.distribute_and_over_or" class="py-name" href="#" onclick="return doclink('link-144', 'distribute_and_over_or', 'link-119');">distribute_and_over_or</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L535"></a><tt class="py-lineno"> 535</tt>  <tt class="py-line">        <tt class="py-name">conj</tt> <tt class="py-op">=</tt> <tt class="py-name">find_if</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-keyword">lambda</tt> <tt id="link-145" class="py-name" targets="Function spade.logic.d()=spade.logic-module.html#d"><a title="spade.logic.d" class="py-name" href="#" onclick="return doclink('link-145', 'd', 'link-145');">d</a></tt><tt class="py-op">:</tt> <tt id="link-146" class="py-name"><a title="spade.logic.d" class="py-name" href="#" onclick="return doclink('link-146', 'd', 'link-145');">d</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&amp;'</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L536"></a><tt class="py-lineno"> 536</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">conj</tt><tt class="py-op">:</tt> </tt>
<a name="L537"></a><tt class="py-lineno"> 537</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt id="link-147" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-147', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L538"></a><tt class="py-lineno"> 538</tt>  <tt class="py-line">        <tt class="py-name">others</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt id="link-148" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-148', 'a', 'link-122');">a</a></tt> <tt class="py-keyword">for</tt> <tt id="link-149" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-149', 'a', 'link-122');">a</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> <tt class="py-keyword">if</tt> <tt id="link-150" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-150', 'a', 'link-122');">a</a></tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">conj</tt><tt class="py-op">]</tt> </tt>
<a name="L539"></a><tt class="py-lineno"> 539</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">others</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L540"></a><tt class="py-lineno"> 540</tt>  <tt class="py-line">            <tt class="py-name">rest</tt> <tt class="py-op">=</tt> <tt class="py-name">others</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L541"></a><tt class="py-lineno"> 541</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L542"></a><tt class="py-lineno"> 542</tt>  <tt class="py-line">            <tt class="py-name">rest</tt> <tt class="py-op">=</tt> <tt id="link-151" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-151', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'|'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">others</tt><tt class="py-op">)</tt> </tt>
<a name="L543"></a><tt class="py-lineno"> 543</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-152" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-152', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-153" class="py-name"><a title="spade.logic.distribute_and_over_or" class="py-name" href="#" onclick="return doclink('link-153', 'distribute_and_over_or', 'link-119');">distribute_and_over_or</a></tt><tt class="py-op">,</tt> </tt>
<a name="L544"></a><tt class="py-lineno"> 544</tt>  <tt class="py-line">                                  <tt class="py-op">[</tt><tt class="py-op">(</tt><tt id="link-154" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-154', 'c', 'link-17');">c</a></tt><tt class="py-op">|</tt><tt class="py-name">rest</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt id="link-155" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-155', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">conj</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L545"></a><tt class="py-lineno"> 545</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&amp;'</tt><tt class="py-op">:</tt> </tt>
<a name="L546"></a><tt class="py-lineno"> 546</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-156" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-156', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-157" class="py-name"><a title="spade.logic.distribute_and_over_or" class="py-name" href="#" onclick="return doclink('link-157', 'distribute_and_over_or', 'link-119');">distribute_and_over_or</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L547"></a><tt class="py-lineno"> 547</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L548"></a><tt class="py-lineno"> 548</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt> </tt>
</div><a name="L549"></a><tt class="py-lineno"> 549</tt>  <tt class="py-line"> </tt>
<a name="L550"></a><tt class="py-lineno"> 550</tt>  <tt class="py-line"><tt id="link-158" class="py-name" targets="Variable spade.logic._NaryExprTable=spade.logic-module.html#_NaryExprTable"><a title="spade.logic._NaryExprTable" class="py-name" href="#" onclick="return doclink('link-158', '_NaryExprTable', 'link-158');">_NaryExprTable</a></tt> <tt class="py-op">=</tt> <tt class="py-op">{</tt><tt class="py-string">'&amp;'</tt><tt class="py-op">:</tt><tt id="link-159" class="py-name"><a title="spade.bdi.TRUE
spade.logic.TRUE" class="py-name" href="#" onclick="return doclink('link-159', 'TRUE', 'link-67');">TRUE</a></tt><tt class="py-op">,</tt> <tt class="py-string">'|'</tt><tt class="py-op">:</tt><tt id="link-160" class="py-name"><a title="spade.bdi.FALSE
spade.logic.FALSE" class="py-name" href="#" onclick="return doclink('link-160', 'FALSE', 'link-68');">FALSE</a></tt><tt class="py-op">,</tt> <tt class="py-string">'+'</tt><tt class="py-op">:</tt><tt id="link-161" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-161', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">,</tt> <tt class="py-string">'*'</tt><tt class="py-op">:</tt><tt id="link-162" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-162', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">}</tt> </tt>
<a name="L551"></a><tt class="py-lineno"> 551</tt>  <tt class="py-line"> </tt>
<a name="NaryExpr"></a><div id="NaryExpr-def"><a name="L552"></a><tt class="py-lineno"> 552</tt> <a class="py-toggle" href="#" id="NaryExpr-toggle" onclick="return toggle('NaryExpr');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#NaryExpr">NaryExpr</a><tt class="py-op">(</tt><tt class="py-param">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-param">args</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="NaryExpr-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="NaryExpr-expanded"><a name="L553"></a><tt class="py-lineno"> 553</tt>  <tt class="py-line">    <tt class="py-docstring">"""Create an Expr, but with an nary, associative op, so we can promote</tt> </tt>
<a name="L554"></a><tt class="py-lineno"> 554</tt>  <tt class="py-line"><tt class="py-docstring">    nested instances of the same op up to the top level.</tt> </tt>
<a name="L555"></a><tt class="py-lineno"> 555</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; NaryExpr('&amp;', (A&amp;B),(B|C),(B&amp;C))</tt> </tt>
<a name="L556"></a><tt class="py-lineno"> 556</tt>  <tt class="py-line"><tt class="py-docstring">    (A &amp; B &amp; (B | C) &amp; B &amp; C)</tt> </tt>
<a name="L557"></a><tt class="py-lineno"> 557</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L558"></a><tt class="py-lineno"> 558</tt>  <tt class="py-line">    <tt class="py-name">arglist</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L559"></a><tt class="py-lineno"> 559</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">arg</tt> <tt class="py-keyword">in</tt> <tt class="py-name">args</tt><tt class="py-op">:</tt> </tt>
<a name="L560"></a><tt class="py-lineno"> 560</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">arg</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-name">op</tt><tt class="py-op">:</tt> <tt class="py-name">arglist</tt><tt class="py-op">.</tt><tt id="link-163" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-163', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">arg</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L561"></a><tt class="py-lineno"> 561</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-name">arglist</tt><tt class="py-op">.</tt><tt id="link-164" class="py-name" targets="Method spade.pyparsing.ParseExpression.append()=spade.pyparsing.ParseExpression-class.html#append"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-164', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt class="py-name">arg</tt><tt class="py-op">)</tt> </tt>
<a name="L562"></a><tt class="py-lineno"> 562</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L563"></a><tt class="py-lineno"> 563</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L564"></a><tt class="py-lineno"> 564</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L565"></a><tt class="py-lineno"> 565</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-165" class="py-name"><a title="spade.logic._NaryExprTable" class="py-name" href="#" onclick="return doclink('link-165', '_NaryExprTable', 'link-158');">_NaryExprTable</a></tt><tt class="py-op">[</tt><tt class="py-name">op</tt><tt class="py-op">]</tt> </tt>
<a name="L566"></a><tt class="py-lineno"> 566</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L567"></a><tt class="py-lineno"> 567</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-166" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-166', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">arglist</tt><tt class="py-op">)</tt> </tt>
</div><a name="L568"></a><tt class="py-lineno"> 568</tt>  <tt class="py-line"> </tt>
<a name="conjuncts"></a><div id="conjuncts-def"><a name="L569"></a><tt class="py-lineno"> 569</tt> <a class="py-toggle" href="#" id="conjuncts-toggle" onclick="return toggle('conjuncts');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#conjuncts">conjuncts</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="conjuncts-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="conjuncts-expanded"><a name="L570"></a><tt class="py-lineno"> 570</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return a list of the conjuncts in the sentence s.</tt> </tt>
<a name="L571"></a><tt class="py-lineno"> 571</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; conjuncts(A &amp; B)</tt> </tt>
<a name="L572"></a><tt class="py-lineno"> 572</tt>  <tt class="py-line"><tt class="py-docstring">    [A, B]</tt> </tt>
<a name="L573"></a><tt class="py-lineno"> 573</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; conjuncts(A | B)</tt> </tt>
<a name="L574"></a><tt class="py-lineno"> 574</tt>  <tt class="py-line"><tt class="py-docstring">    [(A | B)]</tt> </tt>
<a name="L575"></a><tt class="py-lineno"> 575</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L576"></a><tt class="py-lineno"> 576</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt id="link-167" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-167', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&amp;'</tt><tt class="py-op">:</tt>  </tt>
<a name="L577"></a><tt class="py-lineno"> 577</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> </tt>
<a name="L578"></a><tt class="py-lineno"> 578</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L579"></a><tt class="py-lineno"> 579</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt class="py-name">s</tt><tt class="py-op">]</tt> </tt>
</div><a name="L580"></a><tt class="py-lineno"> 580</tt>  <tt class="py-line"> </tt>
<a name="disjuncts"></a><div id="disjuncts-def"><a name="L581"></a><tt class="py-lineno"> 581</tt> <a class="py-toggle" href="#" id="disjuncts-toggle" onclick="return toggle('disjuncts');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#disjuncts">disjuncts</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="disjuncts-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="disjuncts-expanded"><a name="L582"></a><tt class="py-lineno"> 582</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return a list of the disjuncts in the sentence s.</tt> </tt>
<a name="L583"></a><tt class="py-lineno"> 583</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; disjuncts(A | B)</tt> </tt>
<a name="L584"></a><tt class="py-lineno"> 584</tt>  <tt class="py-line"><tt class="py-docstring">    [A, B]</tt> </tt>
<a name="L585"></a><tt class="py-lineno"> 585</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; disjuncts(A &amp; B)</tt> </tt>
<a name="L586"></a><tt class="py-lineno"> 586</tt>  <tt class="py-line"><tt class="py-docstring">    [(A &amp; B)]</tt> </tt>
<a name="L587"></a><tt class="py-lineno"> 587</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L588"></a><tt class="py-lineno"> 588</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt id="link-168" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-168', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'|'</tt><tt class="py-op">:</tt>  </tt>
<a name="L589"></a><tt class="py-lineno"> 589</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">args</tt> </tt>
<a name="L590"></a><tt class="py-lineno"> 590</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L591"></a><tt class="py-lineno"> 591</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt class="py-name">s</tt><tt class="py-op">]</tt> </tt>
</div><a name="L592"></a><tt class="py-lineno"> 592</tt>  <tt class="py-line"> </tt>
<a name="L593"></a><tt class="py-lineno"> 593</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L594"></a><tt class="py-lineno"> 594</tt>  <tt class="py-line"> </tt>
<a name="pl_resolution"></a><div id="pl_resolution-def"><a name="L595"></a><tt class="py-lineno"> 595</tt> <a class="py-toggle" href="#" id="pl_resolution-toggle" onclick="return toggle('pl_resolution');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pl_resolution">pl_resolution</a><tt class="py-op">(</tt><tt class="py-param">KB</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pl_resolution-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pl_resolution-expanded"><a name="L596"></a><tt class="py-lineno"> 596</tt>  <tt class="py-line">    <tt class="py-docstring">"Propositional Logic Resolution: say if alpha follows from KB. [Fig. 7.12]"</tt> </tt>
<a name="L597"></a><tt class="py-lineno"> 597</tt>  <tt class="py-line">    <tt class="py-name">clauses</tt> <tt class="py-op">=</tt> <tt id="link-169" class="py-name" targets="Class spade.logic.KB=spade.logic.KB-class.html"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-169', 'KB', 'link-169');">KB</a></tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt> <tt class="py-op">+</tt> <tt id="link-170" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-170', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-171" class="py-name"><a title="spade.logic.to_cnf" class="py-name" href="#" onclick="return doclink('link-171', 'to_cnf', 'link-14');">to_cnf</a></tt><tt class="py-op">(</tt><tt class="py-op">~</tt><tt class="py-name">alpha</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L598"></a><tt class="py-lineno"> 598</tt>  <tt class="py-line">    <tt class="py-name">new</tt> <tt class="py-op">=</tt> <tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L599"></a><tt class="py-lineno"> 599</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">True</tt><tt class="py-op">:</tt> </tt>
<a name="L600"></a><tt class="py-lineno"> 600</tt>  <tt class="py-line">        <tt class="py-name">n</tt> <tt class="py-op">=</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">)</tt> </tt>
<a name="L601"></a><tt class="py-lineno"> 601</tt>  <tt class="py-line">        <tt class="py-name">pairs</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">clauses</tt><tt class="py-op">[</tt><tt class="py-name">j</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L602"></a><tt class="py-lineno"> 602</tt>  <tt class="py-line">                 <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">n</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">j</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">i</tt><tt class="py-op">+</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-name">n</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L603"></a><tt class="py-lineno"> 603</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-op">(</tt><tt class="py-name">ci</tt><tt class="py-op">,</tt> <tt class="py-name">cj</tt><tt class="py-op">)</tt> <tt class="py-keyword">in</tt> <tt class="py-name">pairs</tt><tt class="py-op">:</tt> </tt>
<a name="L604"></a><tt class="py-lineno"> 604</tt>  <tt class="py-line">            <tt class="py-name">resolvents</tt> <tt class="py-op">=</tt> <tt id="link-172" class="py-name" targets="Function spade.logic.pl_resolve()=spade.logic-module.html#pl_resolve"><a title="spade.logic.pl_resolve" class="py-name" href="#" onclick="return doclink('link-172', 'pl_resolve', 'link-172');">pl_resolve</a></tt><tt class="py-op">(</tt><tt class="py-name">ci</tt><tt class="py-op">,</tt> <tt class="py-name">cj</tt><tt class="py-op">)</tt> </tt>
<a name="L605"></a><tt class="py-lineno"> 605</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-173" class="py-name"><a title="spade.bdi.FALSE
spade.logic.FALSE" class="py-name" href="#" onclick="return doclink('link-173', 'FALSE', 'link-68');">FALSE</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">resolvents</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L606"></a><tt class="py-lineno"> 606</tt>  <tt class="py-line">            <tt class="py-name">new</tt> <tt class="py-op">=</tt> <tt class="py-name">new</tt><tt class="py-op">.</tt><tt class="py-name">union</tt><tt class="py-op">(</tt><tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-name">resolvents</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L607"></a><tt class="py-lineno"> 607</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">new</tt><tt class="py-op">.</tt><tt class="py-name">issubset</tt><tt class="py-op">(</tt><tt class="py-name">set</tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
<a name="L608"></a><tt class="py-lineno"> 608</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt id="link-174" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-174', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">new</tt><tt class="py-op">:</tt> </tt>
<a name="L609"></a><tt class="py-lineno"> 609</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-175" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-175', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">not</tt> <tt class="py-keyword">in</tt> <tt class="py-name">clauses</tt><tt class="py-op">:</tt> <tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt id="link-176" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-176', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt id="link-177" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-177', 'c', 'link-17');">c</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L610"></a><tt class="py-lineno"> 610</tt>  <tt class="py-line"> </tt>
<a name="pl_resolve"></a><div id="pl_resolve-def"><a name="L611"></a><tt class="py-lineno"> 611</tt> <a class="py-toggle" href="#" id="pl_resolve-toggle" onclick="return toggle('pl_resolve');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pl_resolve">pl_resolve</a><tt class="py-op">(</tt><tt class="py-param">ci</tt><tt class="py-op">,</tt> <tt class="py-param">cj</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pl_resolve-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pl_resolve-expanded"><a name="L612"></a><tt class="py-lineno"> 612</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return all clauses that can be obtained by resolving clauses ci and cj.</tt> </tt>
<a name="L613"></a><tt class="py-lineno"> 613</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; for res in pl_resolve(to_cnf(A|B|C), to_cnf(~B|~C|F)):</tt> </tt>
<a name="L614"></a><tt class="py-lineno"> 614</tt>  <tt class="py-line"><tt class="py-docstring">    ...    ppset(disjuncts(res))</tt> </tt>
<a name="L615"></a><tt class="py-lineno"> 615</tt>  <tt class="py-line"><tt class="py-docstring">    set([A, C, F, ~C])</tt> </tt>
<a name="L616"></a><tt class="py-lineno"> 616</tt>  <tt class="py-line"><tt class="py-docstring">    set([A, B, F, ~B])</tt> </tt>
<a name="L617"></a><tt class="py-lineno"> 617</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L618"></a><tt class="py-lineno"> 618</tt>  <tt class="py-line">    <tt class="py-name">clauses</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L619"></a><tt class="py-lineno"> 619</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">di</tt> <tt class="py-keyword">in</tt> <tt id="link-178" class="py-name" targets="Function spade.logic.disjuncts()=spade.logic-module.html#disjuncts"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-178', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt class="py-name">ci</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L620"></a><tt class="py-lineno"> 620</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">dj</tt> <tt class="py-keyword">in</tt> <tt id="link-179" class="py-name"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-179', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt class="py-name">cj</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L621"></a><tt class="py-lineno"> 621</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">di</tt> <tt class="py-op">==</tt> <tt class="py-op">~</tt><tt class="py-name">dj</tt> <tt class="py-keyword">or</tt> <tt class="py-op">~</tt><tt class="py-name">di</tt> <tt class="py-op">==</tt> <tt class="py-name">dj</tt><tt class="py-op">:</tt> </tt>
<a name="L622"></a><tt class="py-lineno"> 622</tt>  <tt class="py-line">                <tt class="py-name">dnew</tt> <tt class="py-op">=</tt> <tt class="py-name">unique</tt><tt class="py-op">(</tt><tt class="py-name">removeall</tt><tt class="py-op">(</tt><tt class="py-name">di</tt><tt class="py-op">,</tt> <tt id="link-180" class="py-name"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-180', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt class="py-name">ci</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt>  </tt>
<a name="L623"></a><tt class="py-lineno"> 623</tt>  <tt class="py-line">                              <tt class="py-name">removeall</tt><tt class="py-op">(</tt><tt class="py-name">dj</tt><tt class="py-op">,</tt> <tt id="link-181" class="py-name"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-181', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt class="py-name">cj</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L624"></a><tt class="py-lineno"> 624</tt>  <tt class="py-line">                <tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt id="link-182" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-182', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt id="link-183" class="py-name"><a title="spade.logic.NaryExpr" class="py-name" href="#" onclick="return doclink('link-183', 'NaryExpr', 'link-134');">NaryExpr</a></tt><tt class="py-op">(</tt><tt class="py-string">'|'</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">dnew</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L625"></a><tt class="py-lineno"> 625</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">clauses</tt> </tt>
</div><a name="L626"></a><tt class="py-lineno"> 626</tt>  <tt class="py-line"> </tt>
<a name="L627"></a><tt class="py-lineno"> 627</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L628"></a><tt class="py-lineno"> 628</tt>  <tt class="py-line"> </tt>
<a name="PropHornKB"></a><div id="PropHornKB-def"><a name="L629"></a><tt class="py-lineno"> 629</tt> <a class="py-toggle" href="#" id="PropHornKB-toggle" onclick="return toggle('PropHornKB');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="spade.logic.PropHornKB-class.html">PropHornKB</a><tt class="py-op">(</tt><tt class="py-base-class">PropKB</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropHornKB-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="PropHornKB-expanded"><a name="L630"></a><tt class="py-lineno"> 630</tt>  <tt class="py-line">    <tt class="py-docstring">"A KB of Propositional Horn clauses."</tt> </tt>
<a name="L631"></a><tt class="py-lineno"> 631</tt>  <tt class="py-line"> </tt>
<a name="PropHornKB.tell"></a><div id="PropHornKB.tell-def"><a name="L632"></a><tt class="py-lineno"> 632</tt> <a class="py-toggle" href="#" id="PropHornKB.tell-toggle" onclick="return toggle('PropHornKB.tell');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropHornKB-class.html#tell">tell</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropHornKB.tell-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="PropHornKB.tell-expanded"><a name="L633"></a><tt class="py-lineno"> 633</tt>  <tt class="py-line">        <tt class="py-docstring">"Add a Horn Clauses to this KB."</tt> </tt>
<a name="L634"></a><tt class="py-lineno"> 634</tt>  <tt class="py-line">        <tt class="py-name">op</tt> <tt class="py-op">=</tt> <tt class="py-name">sentence</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> </tt>
<a name="L635"></a><tt class="py-lineno"> 635</tt>  <tt class="py-line">        <tt class="py-keyword">assert</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt> <tt class="py-keyword">or</tt> <tt id="link-184" class="py-name"><a title="spade.logic.is_prop_symbol" class="py-name" href="#" onclick="return doclink('link-184', 'is_prop_symbol', 'link-97');">is_prop_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-string">"Must be Horn Clause"</tt> </tt>
<a name="L636"></a><tt class="py-lineno"> 636</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt id="link-185" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-185', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt> </tt>
</div><a name="L637"></a><tt class="py-lineno"> 637</tt>  <tt class="py-line"> </tt>
<a name="PropHornKB.ask_generator"></a><div id="PropHornKB.ask_generator-def"><a name="L638"></a><tt class="py-lineno"> 638</tt> <a class="py-toggle" href="#" id="PropHornKB.ask_generator-toggle" onclick="return toggle('PropHornKB.ask_generator');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropHornKB-class.html#ask_generator">ask_generator</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
</div><a name="L639"></a><tt class="py-lineno"> 639</tt>  <tt class="py-line">        <tt class="py-docstring">"Yield the empty substitution if KB implies query; else False"</tt> </tt>
<a name="L640"></a><tt class="py-lineno"> 640</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt id="link-186" class="py-name" targets="Function spade.logic.pl_fc_entails()=spade.logic-module.html#pl_fc_entails"><a title="spade.logic.pl_fc_entails" class="py-name" href="#" onclick="return doclink('link-186', 'pl_fc_entails', 'link-186');">pl_fc_entails</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L641"></a><tt class="py-lineno"> 641</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> </tt>
<a name="L642"></a><tt class="py-lineno"> 642</tt>  <tt class="py-line">        <tt class="py-keyword">yield</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
</div><a name="L643"></a><tt class="py-lineno"> 643</tt>  <tt class="py-line"> </tt>
<a name="PropHornKB.retract"></a><div id="PropHornKB.retract-def"><a name="L644"></a><tt class="py-lineno"> 644</tt> <a class="py-toggle" href="#" id="PropHornKB.retract-toggle" onclick="return toggle('PropHornKB.retract');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropHornKB-class.html#retract">retract</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropHornKB.retract-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="PropHornKB.retract-expanded"><a name="L645"></a><tt class="py-lineno"> 645</tt>  <tt class="py-line">        <tt class="py-docstring">"Remove the sentence's clauses from the KB"</tt> </tt>
<a name="L646"></a><tt class="py-lineno"> 646</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt id="link-187" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-187', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt id="link-188" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-188', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-189" class="py-name"><a title="spade.logic.to_cnf" class="py-name" href="#" onclick="return doclink('link-189', 'to_cnf', 'link-14');">to_cnf</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L647"></a><tt class="py-lineno"> 647</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-190" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-190', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L648"></a><tt class="py-lineno"> 648</tt>  <tt class="py-line">                <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt class="py-name">remove</tt><tt class="py-op">(</tt><tt id="link-191" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-191', 'c', 'link-17');">c</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L649"></a><tt class="py-lineno"> 649</tt>  <tt class="py-line"> </tt>
<a name="PropHornKB.clauses_with_premise"></a><div id="PropHornKB.clauses_with_premise-def"><a name="L650"></a><tt class="py-lineno"> 650</tt> <a class="py-toggle" href="#" id="PropHornKB.clauses_with_premise-toggle" onclick="return toggle('PropHornKB.clauses_with_premise');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.PropHornKB-class.html#clauses_with_premise">clauses_with_premise</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">p</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="PropHornKB.clauses_with_premise-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="PropHornKB.clauses_with_premise-expanded"><a name="L651"></a><tt class="py-lineno"> 651</tt>  <tt class="py-line">        <tt class="py-docstring">"""The list of clauses in KB that have p in the premise.</tt> </tt>
<a name="L652"></a><tt class="py-lineno"> 652</tt>  <tt class="py-line"><tt class="py-docstring">        This could be cached away for O(1) speed, but we'll recompute it."""</tt> </tt>
<a name="L653"></a><tt class="py-lineno"> 653</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt id="link-192" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-192', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">for</tt> <tt id="link-193" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-193', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt>  </tt>
<a name="L654"></a><tt class="py-lineno"> 654</tt>  <tt class="py-line">                <tt class="py-keyword">if</tt> <tt id="link-194" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-194', 'c', 'link-17');">c</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt> <tt class="py-keyword">and</tt> <tt class="py-name">p</tt> <tt class="py-keyword">in</tt> <tt id="link-195" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-195', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-196" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-196', 'c', 'link-17');">c</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
</div></div><a name="L655"></a><tt class="py-lineno"> 655</tt>  <tt class="py-line"> </tt>
<a name="pl_fc_entails"></a><div id="pl_fc_entails-def"><a name="L656"></a><tt class="py-lineno"> 656</tt> <a class="py-toggle" href="#" id="pl_fc_entails-toggle" onclick="return toggle('pl_fc_entails');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pl_fc_entails">pl_fc_entails</a><tt class="py-op">(</tt><tt class="py-param">KB</tt><tt class="py-op">,</tt> <tt class="py-param">q</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pl_fc_entails-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pl_fc_entails-expanded"><a name="L657"></a><tt class="py-lineno"> 657</tt>  <tt class="py-line">    <tt class="py-docstring">"""Use forward chaining to see if a HornKB entails symbol q. [Fig. 7.14]</tt> </tt>
<a name="L658"></a><tt class="py-lineno"> 658</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; pl_fc_entails(Fig[7,15], expr('Q'))</tt> </tt>
<a name="L659"></a><tt class="py-lineno"> 659</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L660"></a><tt class="py-lineno"> 660</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L661"></a><tt class="py-lineno"> 661</tt>  <tt class="py-line">    <tt id="link-197" class="py-name" targets="Variable spade.xmpp.commands.Command_Handler_Prototype.count=spade.xmpp.commands.Command_Handler_Prototype-class.html#count"><a title="spade.xmpp.commands.Command_Handler_Prototype.count" class="py-name" href="#" onclick="return doclink('link-197', 'count', 'link-197');">count</a></tt> <tt class="py-op">=</tt> <tt class="py-name">dict</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-op">(</tt><tt id="link-198" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-198', 'c', 'link-17');">c</a></tt><tt class="py-op">,</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt id="link-199" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-199', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-200" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-200', 'c', 'link-17');">c</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt id="link-201" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-201', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt id="link-202" class="py-name"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-202', 'KB', 'link-169');">KB</a></tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt> </tt>
<a name="L662"></a><tt class="py-lineno"> 662</tt>  <tt class="py-line">                                                 <tt class="py-keyword">if</tt> <tt id="link-203" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-203', 'c', 'link-17');">c</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L663"></a><tt class="py-lineno"> 663</tt>  <tt class="py-line">    <tt class="py-name">inferred</tt> <tt class="py-op">=</tt> <tt class="py-name">DefaultDict</tt><tt class="py-op">(</tt><tt class="py-name">False</tt><tt class="py-op">)</tt> </tt>
<a name="L664"></a><tt class="py-lineno"> 664</tt>  <tt class="py-line">    <tt class="py-name">agenda</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">s</tt> <tt class="py-keyword">for</tt> <tt class="py-name">s</tt> <tt class="py-keyword">in</tt> <tt id="link-204" class="py-name"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-204', 'KB', 'link-169');">KB</a></tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt> <tt class="py-keyword">if</tt> <tt id="link-205" class="py-name"><a title="spade.logic.is_prop_symbol" class="py-name" href="#" onclick="return doclink('link-205', 'is_prop_symbol', 'link-97');">is_prop_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L665"></a><tt class="py-lineno"> 665</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">q</tt> <tt class="py-keyword">in</tt> <tt class="py-name">agenda</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L666"></a><tt class="py-lineno"> 666</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">agenda</tt><tt class="py-op">:</tt> </tt>
<a name="L667"></a><tt class="py-lineno"> 667</tt>  <tt class="py-line">        <tt class="py-name">p</tt> <tt class="py-op">=</tt> <tt class="py-name">agenda</tt><tt class="py-op">.</tt><tt class="py-name">pop</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L668"></a><tt class="py-lineno"> 668</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">inferred</tt><tt class="py-op">[</tt><tt class="py-name">p</tt><tt class="py-op">]</tt><tt class="py-op">:</tt> </tt>
<a name="L669"></a><tt class="py-lineno"> 669</tt>  <tt class="py-line">            <tt class="py-name">inferred</tt><tt class="py-op">[</tt><tt class="py-name">p</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">True</tt> </tt>
<a name="L670"></a><tt class="py-lineno"> 670</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt id="link-206" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-206', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt id="link-207" class="py-name"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-207', 'KB', 'link-169');">KB</a></tt><tt class="py-op">.</tt><tt id="link-208" class="py-name" targets="Method spade.logic.PropHornKB.clauses_with_premise()=spade.logic.PropHornKB-class.html#clauses_with_premise"><a title="spade.logic.PropHornKB.clauses_with_premise" class="py-name" href="#" onclick="return doclink('link-208', 'clauses_with_premise', 'link-208');">clauses_with_premise</a></tt><tt class="py-op">(</tt><tt class="py-name">p</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L671"></a><tt class="py-lineno"> 671</tt>  <tt class="py-line">                <tt id="link-209" class="py-name"><a title="spade.xmpp.commands.Command_Handler_Prototype.count" class="py-name" href="#" onclick="return doclink('link-209', 'count', 'link-197');">count</a></tt><tt class="py-op">[</tt><tt id="link-210" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-210', 'c', 'link-17');">c</a></tt><tt class="py-op">]</tt> <tt class="py-op">-=</tt> <tt class="py-number">1</tt> </tt>
<a name="L672"></a><tt class="py-lineno"> 672</tt>  <tt class="py-line">                <tt class="py-keyword">if</tt> <tt id="link-211" class="py-name"><a title="spade.xmpp.commands.Command_Handler_Prototype.count" class="py-name" href="#" onclick="return doclink('link-211', 'count', 'link-197');">count</a></tt><tt class="py-op">[</tt><tt id="link-212" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-212', 'c', 'link-17');">c</a></tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L673"></a><tt class="py-lineno"> 673</tt>  <tt class="py-line">                    <tt class="py-keyword">if</tt> <tt id="link-213" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-213', 'c', 'link-17');">c</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">==</tt> <tt class="py-name">q</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L674"></a><tt class="py-lineno"> 674</tt>  <tt class="py-line">                    <tt class="py-name">agenda</tt><tt class="py-op">.</tt><tt id="link-214" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-214', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt id="link-215" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-215', 'c', 'link-17');">c</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L675"></a><tt class="py-lineno"> 675</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
</div><a name="L676"></a><tt class="py-lineno"> 676</tt>  <tt class="py-line"> </tt>
<a name="L677"></a><tt class="py-lineno"> 677</tt>  <tt class="py-line"><tt class="py-comment">## Wumpus World example [Fig. 7.13]</tt> </tt>
<a name="L678"></a><tt class="py-lineno"> 678</tt>  <tt class="py-line"><tt class="py-comment">#Fig[7,13] = expr("(B11 &lt;=&gt; (P12 | P21))  &amp;  ~B11")</tt> </tt>
<a name="L679"></a><tt class="py-lineno"> 679</tt>  <tt class="py-line"> </tt>
<a name="L680"></a><tt class="py-lineno"> 680</tt>  <tt class="py-line"><tt class="py-comment">## Propositional Logic Forward Chaining example [Fig. 7.15]</tt> </tt>
<a name="L681"></a><tt class="py-lineno"> 681</tt>  <tt class="py-line"><tt class="py-comment">#Fig[7,15] = PropHornKB()</tt> </tt>
<a name="L682"></a><tt class="py-lineno"> 682</tt>  <tt class="py-line"><tt class="py-comment">#for s in "P&gt;&gt;Q   (L&amp;M)&gt;&gt;P   (B&amp;L)&gt;&gt;M   (A&amp;P)&gt;&gt;L   (A&amp;B)&gt;&gt;L   A   B".split(): </tt> </tt>
<a name="L683"></a><tt class="py-lineno"> 683</tt>  <tt class="py-line"><tt class="py-comment">#    Fig[7,15].tell(expr(s))</tt> </tt>
<a name="L684"></a><tt class="py-lineno"> 684</tt>  <tt class="py-line"> </tt>
<a name="L685"></a><tt class="py-lineno"> 685</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L686"></a><tt class="py-lineno"> 686</tt>  <tt class="py-line"> </tt>
<a name="L687"></a><tt class="py-lineno"> 687</tt>  <tt class="py-line"><tt class="py-comment"># DPLL-Satisfiable [Fig. 7.16]</tt> </tt>
<a name="L688"></a><tt class="py-lineno"> 688</tt>  <tt class="py-line"> </tt>
<a name="dpll_satisfiable"></a><div id="dpll_satisfiable-def"><a name="L689"></a><tt class="py-lineno"> 689</tt> <a class="py-toggle" href="#" id="dpll_satisfiable-toggle" onclick="return toggle('dpll_satisfiable');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#dpll_satisfiable">dpll_satisfiable</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="dpll_satisfiable-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="dpll_satisfiable-expanded"><a name="L690"></a><tt class="py-lineno"> 690</tt>  <tt class="py-line">    <tt class="py-docstring">"""Check satisfiability of a propositional sentence.</tt> </tt>
<a name="L691"></a><tt class="py-lineno"> 691</tt>  <tt class="py-line"><tt class="py-docstring">    This differs from the book code in two ways: (1) it returns a model</tt> </tt>
<a name="L692"></a><tt class="py-lineno"> 692</tt>  <tt class="py-line"><tt class="py-docstring">    rather than True when it succeeds; this is more useful. (2) The</tt> </tt>
<a name="L693"></a><tt class="py-lineno"> 693</tt>  <tt class="py-line"><tt class="py-docstring">    function find_pure_symbol is passed a list of unknown clauses, rather</tt> </tt>
<a name="L694"></a><tt class="py-lineno"> 694</tt>  <tt class="py-line"><tt class="py-docstring">    than a list of all clauses and the model; this is more efficient.</tt> </tt>
<a name="L695"></a><tt class="py-lineno"> 695</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppsubst(dpll_satisfiable(A&amp;~B))</tt> </tt>
<a name="L696"></a><tt class="py-lineno"> 696</tt>  <tt class="py-line"><tt class="py-docstring">    {A: True, B: False}</tt> </tt>
<a name="L697"></a><tt class="py-lineno"> 697</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; dpll_satisfiable(P&amp;~P)</tt> </tt>
<a name="L698"></a><tt class="py-lineno"> 698</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L699"></a><tt class="py-lineno"> 699</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L700"></a><tt class="py-lineno"> 700</tt>  <tt class="py-line">    <tt class="py-name">clauses</tt> <tt class="py-op">=</tt> <tt id="link-216" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-216', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-217" class="py-name"><a title="spade.logic.to_cnf" class="py-name" href="#" onclick="return doclink('link-217', 'to_cnf', 'link-14');">to_cnf</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L701"></a><tt class="py-lineno"> 701</tt>  <tt class="py-line">    <tt class="py-name">symbols</tt> <tt class="py-op">=</tt> <tt id="link-218" class="py-name"><a title="spade.logic.prop_symbols" class="py-name" href="#" onclick="return doclink('link-218', 'prop_symbols', 'link-85');">prop_symbols</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L702"></a><tt class="py-lineno"> 702</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-219" class="py-name" targets="Function spade.logic.dpll()=spade.logic-module.html#dpll"><a title="spade.logic.dpll" class="py-name" href="#" onclick="return doclink('link-219', 'dpll', 'link-219');">dpll</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">symbols</tt><tt class="py-op">,</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">)</tt> </tt>
</div><a name="L703"></a><tt class="py-lineno"> 703</tt>  <tt class="py-line">  </tt>
<a name="dpll"></a><div id="dpll-def"><a name="L704"></a><tt class="py-lineno"> 704</tt> <a class="py-toggle" href="#" id="dpll-toggle" onclick="return toggle('dpll');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#dpll">dpll</a><tt class="py-op">(</tt><tt class="py-param">clauses</tt><tt class="py-op">,</tt> <tt class="py-param">symbols</tt><tt class="py-op">,</tt> <tt class="py-param">model</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="dpll-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="dpll-expanded"><a name="L705"></a><tt class="py-lineno"> 705</tt>  <tt class="py-line">    <tt class="py-docstring">"See if the clauses are true in a partial model."</tt> </tt>
<a name="L706"></a><tt class="py-lineno"> 706</tt>  <tt class="py-line">    <tt class="py-name">unknown_clauses</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> <tt class="py-comment">## clauses with an unknown truth value</tt> </tt>
<a name="L707"></a><tt class="py-lineno"> 707</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt id="link-220" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-220', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L708"></a><tt class="py-lineno"> 708</tt>  <tt class="py-line">        <tt class="py-name">val</tt> <tt class="py-op">=</tt>  <tt id="link-221" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-221', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt id="link-222" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-222', 'c', 'link-17');">c</a></tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L709"></a><tt class="py-lineno"> 709</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">val</tt> <tt class="py-op">==</tt> <tt class="py-name">False</tt><tt class="py-op">:</tt> </tt>
<a name="L710"></a><tt class="py-lineno"> 710</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
<a name="L711"></a><tt class="py-lineno"> 711</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">val</tt> <tt class="py-op">!=</tt> <tt class="py-name">True</tt><tt class="py-op">:</tt>  </tt>
<a name="L712"></a><tt class="py-lineno"> 712</tt>  <tt class="py-line">            <tt class="py-name">unknown_clauses</tt><tt class="py-op">.</tt><tt id="link-223" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-223', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt id="link-224" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-224', 'c', 'link-17');">c</a></tt><tt class="py-op">)</tt> </tt>
<a name="L713"></a><tt class="py-lineno"> 713</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">unknown_clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L714"></a><tt class="py-lineno"> 714</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">model</tt> </tt>
<a name="L715"></a><tt class="py-lineno"> 715</tt>  <tt class="py-line">    <tt id="link-225" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-225', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">value</tt> <tt class="py-op">=</tt> <tt id="link-226" class="py-name" targets="Function spade.logic.find_pure_symbol()=spade.logic-module.html#find_pure_symbol"><a title="spade.logic.find_pure_symbol" class="py-name" href="#" onclick="return doclink('link-226', 'find_pure_symbol', 'link-226');">find_pure_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">symbols</tt><tt class="py-op">,</tt> <tt class="py-name">unknown_clauses</tt><tt class="py-op">)</tt> </tt>
<a name="L716"></a><tt class="py-lineno"> 716</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-227" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-227', 'P', 'link-78');">P</a></tt><tt class="py-op">:</tt> </tt>
<a name="L717"></a><tt class="py-lineno"> 717</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-228" class="py-name"><a title="spade.logic.dpll" class="py-name" href="#" onclick="return doclink('link-228', 'dpll', 'link-219');">dpll</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">removeall</tt><tt class="py-op">(</tt><tt id="link-229" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-229', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">symbols</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt id="link-230" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-230', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt id="link-231" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-231', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">value</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L718"></a><tt class="py-lineno"> 718</tt>  <tt class="py-line">    <tt id="link-232" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-232', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">value</tt> <tt class="py-op">=</tt> <tt id="link-233" class="py-name" targets="Function spade.logic.find_unit_clause()=spade.logic-module.html#find_unit_clause"><a title="spade.logic.find_unit_clause" class="py-name" href="#" onclick="return doclink('link-233', 'find_unit_clause', 'link-233');">find_unit_clause</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt> </tt>
<a name="L719"></a><tt class="py-lineno"> 719</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-234" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-234', 'P', 'link-78');">P</a></tt><tt class="py-op">:</tt> </tt>
<a name="L720"></a><tt class="py-lineno"> 720</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-235" class="py-name"><a title="spade.logic.dpll" class="py-name" href="#" onclick="return doclink('link-235', 'dpll', 'link-219');">dpll</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">removeall</tt><tt class="py-op">(</tt><tt id="link-236" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-236', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">symbols</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt id="link-237" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-237', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt id="link-238" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-238', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">value</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L721"></a><tt class="py-lineno"> 721</tt>  <tt class="py-line">    <tt id="link-239" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-239', 'P', 'link-78');">P</a></tt> <tt class="py-op">=</tt> <tt class="py-name">symbols</tt><tt class="py-op">.</tt><tt class="py-name">pop</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L722"></a><tt class="py-lineno"> 722</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-240" class="py-name"><a title="spade.logic.dpll" class="py-name" href="#" onclick="return doclink('link-240', 'dpll', 'link-219');">dpll</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">symbols</tt><tt class="py-op">,</tt> <tt id="link-241" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-241', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt id="link-242" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-242', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">True</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> </tt>
<a name="L723"></a><tt class="py-lineno"> 723</tt>  <tt class="py-line">            <tt id="link-243" class="py-name"><a title="spade.logic.dpll" class="py-name" href="#" onclick="return doclink('link-243', 'dpll', 'link-219');">dpll</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">,</tt> <tt class="py-name">symbols</tt><tt class="py-op">,</tt> <tt id="link-244" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-244', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">model</tt><tt class="py-op">,</tt> <tt id="link-245" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-245', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L724"></a><tt class="py-lineno"> 724</tt>  <tt class="py-line">  </tt>
<a name="find_pure_symbol"></a><div id="find_pure_symbol-def"><a name="L725"></a><tt class="py-lineno"> 725</tt> <a class="py-toggle" href="#" id="find_pure_symbol-toggle" onclick="return toggle('find_pure_symbol');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#find_pure_symbol">find_pure_symbol</a><tt class="py-op">(</tt><tt class="py-param">symbols</tt><tt class="py-op">,</tt> <tt class="py-param">unknown_clauses</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="find_pure_symbol-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="find_pure_symbol-expanded"><a name="L726"></a><tt class="py-lineno"> 726</tt>  <tt class="py-line">    <tt class="py-docstring">"""Find a symbol and its value if it appears only as a positive literal</tt> </tt>
<a name="L727"></a><tt class="py-lineno"> 727</tt>  <tt class="py-line"><tt class="py-docstring">    (or only as a negative) in clauses.</tt> </tt>
<a name="L728"></a><tt class="py-lineno"> 728</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; find_pure_symbol([A, B, C], [A|~B,~B|~C,C|A])</tt> </tt>
<a name="L729"></a><tt class="py-lineno"> 729</tt>  <tt class="py-line"><tt class="py-docstring">    (A, True)</tt> </tt>
<a name="L730"></a><tt class="py-lineno"> 730</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L731"></a><tt class="py-lineno"> 731</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">s</tt> <tt class="py-keyword">in</tt> <tt class="py-name">symbols</tt><tt class="py-op">:</tt> </tt>
<a name="L732"></a><tt class="py-lineno"> 732</tt>  <tt class="py-line">        <tt class="py-name">found_pos</tt><tt class="py-op">,</tt> <tt class="py-name">found_neg</tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-name">False</tt> </tt>
<a name="L733"></a><tt class="py-lineno"> 733</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt id="link-246" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-246', 'c', 'link-17');">c</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">unknown_clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L734"></a><tt class="py-lineno"> 734</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">found_pos</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt> <tt class="py-keyword">in</tt> <tt id="link-247" class="py-name"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-247', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt id="link-248" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-248', 'c', 'link-17');">c</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-name">found_pos</tt> <tt class="py-op">=</tt> <tt class="py-name">True</tt> </tt>
<a name="L735"></a><tt class="py-lineno"> 735</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">found_neg</tt> <tt class="py-keyword">and</tt> <tt class="py-op">~</tt><tt class="py-name">s</tt> <tt class="py-keyword">in</tt> <tt id="link-249" class="py-name"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-249', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt id="link-250" class="py-name"><a title="spade.ACLParser.c
spade.AMS.c
spade.DF.c
spade.SL0Parser.c
spade.pyparsing.c" class="py-name" href="#" onclick="return doclink('link-250', 'c', 'link-17');">c</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> <tt class="py-name">found_neg</tt> <tt class="py-op">=</tt> <tt class="py-name">True</tt> </tt>
<a name="L736"></a><tt class="py-lineno"> 736</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">found_pos</tt> <tt class="py-op">!=</tt> <tt class="py-name">found_neg</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">found_pos</tt> </tt>
<a name="L737"></a><tt class="py-lineno"> 737</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt> </tt>
</div><a name="L738"></a><tt class="py-lineno"> 738</tt>  <tt class="py-line"> </tt>
<a name="find_unit_clause"></a><div id="find_unit_clause-def"><a name="L739"></a><tt class="py-lineno"> 739</tt> <a class="py-toggle" href="#" id="find_unit_clause-toggle" onclick="return toggle('find_unit_clause');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#find_unit_clause">find_unit_clause</a><tt class="py-op">(</tt><tt class="py-param">clauses</tt><tt class="py-op">,</tt> <tt class="py-param">model</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="find_unit_clause-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="find_unit_clause-expanded"><a name="L740"></a><tt class="py-lineno"> 740</tt>  <tt class="py-line">    <tt class="py-docstring">"""A unit clause has only 1 variable that is not bound in the model.</tt> </tt>
<a name="L741"></a><tt class="py-lineno"> 741</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; find_unit_clause([A|B|C, B|~C, A|~B], {A:True})</tt> </tt>
<a name="L742"></a><tt class="py-lineno"> 742</tt>  <tt class="py-line"><tt class="py-docstring">    (B, False)</tt> </tt>
<a name="L743"></a><tt class="py-lineno"> 743</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L744"></a><tt class="py-lineno"> 744</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">clause</tt> <tt class="py-keyword">in</tt> <tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L745"></a><tt class="py-lineno"> 745</tt>  <tt class="py-line">        <tt class="py-name">num_not_in_model</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L746"></a><tt class="py-lineno"> 746</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">literal</tt> <tt class="py-keyword">in</tt> <tt id="link-251" class="py-name"><a title="spade.logic.disjuncts" class="py-name" href="#" onclick="return doclink('link-251', 'disjuncts', 'link-178');">disjuncts</a></tt><tt class="py-op">(</tt><tt class="py-name">clause</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L747"></a><tt class="py-lineno"> 747</tt>  <tt class="py-line">            <tt class="py-name">sym</tt> <tt class="py-op">=</tt> <tt id="link-252" class="py-name" targets="Function spade.logic.literal_symbol()=spade.logic-module.html#literal_symbol"><a title="spade.logic.literal_symbol" class="py-name" href="#" onclick="return doclink('link-252', 'literal_symbol', 'link-252');">literal_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">literal</tt><tt class="py-op">)</tt> </tt>
<a name="L748"></a><tt class="py-lineno"> 748</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt class="py-name">sym</tt> <tt class="py-keyword">not</tt> <tt class="py-keyword">in</tt> <tt class="py-name">model</tt><tt class="py-op">:</tt> </tt>
<a name="L749"></a><tt class="py-lineno"> 749</tt>  <tt class="py-line">                <tt class="py-name">num_not_in_model</tt> <tt class="py-op">+=</tt> <tt class="py-number">1</tt> </tt>
<a name="L750"></a><tt class="py-lineno"> 750</tt>  <tt class="py-line">                <tt id="link-253" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-253', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">value</tt> <tt class="py-op">=</tt> <tt class="py-name">sym</tt><tt class="py-op">,</tt> <tt class="py-op">(</tt><tt class="py-name">literal</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">!=</tt> <tt class="py-string">'~'</tt><tt class="py-op">)</tt> </tt>
<a name="L751"></a><tt class="py-lineno"> 751</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">num_not_in_model</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> </tt>
<a name="L752"></a><tt class="py-lineno"> 752</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt id="link-254" class="py-name"><a title="spade.bdi.P
spade.logic.P" class="py-name" href="#" onclick="return doclink('link-254', 'P', 'link-78');">P</a></tt><tt class="py-op">,</tt> <tt class="py-name">value</tt> </tt>
<a name="L753"></a><tt class="py-lineno"> 753</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">None</tt><tt class="py-op">,</tt> <tt class="py-name">None</tt> </tt>
</div><a name="L754"></a><tt class="py-lineno"> 754</tt>  <tt class="py-line">                 </tt>
<a name="L755"></a><tt class="py-lineno"> 755</tt>  <tt class="py-line"> </tt>
<a name="literal_symbol"></a><div id="literal_symbol-def"><a name="L756"></a><tt class="py-lineno"> 756</tt> <a class="py-toggle" href="#" id="literal_symbol-toggle" onclick="return toggle('literal_symbol');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#literal_symbol">literal_symbol</a><tt class="py-op">(</tt><tt class="py-param">literal</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="literal_symbol-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="literal_symbol-expanded"><a name="L757"></a><tt class="py-lineno"> 757</tt>  <tt class="py-line">    <tt class="py-docstring">"""The symbol in this literal (without the negation).</tt> </tt>
<a name="L758"></a><tt class="py-lineno"> 758</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; literal_symbol(P)</tt> </tt>
<a name="L759"></a><tt class="py-lineno"> 759</tt>  <tt class="py-line"><tt class="py-docstring">    P</tt> </tt>
<a name="L760"></a><tt class="py-lineno"> 760</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; literal_symbol(~P)</tt> </tt>
<a name="L761"></a><tt class="py-lineno"> 761</tt>  <tt class="py-line"><tt class="py-docstring">    P</tt> </tt>
<a name="L762"></a><tt class="py-lineno"> 762</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L763"></a><tt class="py-lineno"> 763</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">literal</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'~'</tt><tt class="py-op">:</tt> </tt>
<a name="L764"></a><tt class="py-lineno"> 764</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">literal</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L765"></a><tt class="py-lineno"> 765</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L766"></a><tt class="py-lineno"> 766</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">literal</tt> </tt>
</div><a name="L767"></a><tt class="py-lineno"> 767</tt>  <tt class="py-line">         </tt>
<a name="L768"></a><tt class="py-lineno"> 768</tt>  <tt class="py-line"> </tt>
<a name="L769"></a><tt class="py-lineno"> 769</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L770"></a><tt class="py-lineno"> 770</tt>  <tt class="py-line"><tt class="py-comment"># Walk-SAT [Fig. 7.17]</tt> </tt>
<a name="L771"></a><tt class="py-lineno"> 771</tt>  <tt class="py-line"> </tt>
<a name="WalkSAT"></a><div id="WalkSAT-def"><a name="L772"></a><tt class="py-lineno"> 772</tt> <a class="py-toggle" href="#" id="WalkSAT-toggle" onclick="return toggle('WalkSAT');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#WalkSAT">WalkSAT</a><tt class="py-op">(</tt><tt class="py-param">clauses</tt><tt class="py-op">,</tt> <tt class="py-param">p</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">max_flips</tt><tt class="py-op">=</tt><tt class="py-number">10000</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="WalkSAT-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="WalkSAT-expanded"><a name="L773"></a><tt class="py-lineno"> 773</tt>  <tt class="py-line">    <tt class="py-comment">## model is a random assignment of true/false to the symbols in clauses</tt> </tt>
<a name="L774"></a><tt class="py-lineno"> 774</tt>  <tt class="py-line">    <tt class="py-comment">## See ~/aima1e/print1/manual/knowledge+logic-answers.tex ???</tt> </tt>
<a name="L775"></a><tt class="py-lineno"> 775</tt>  <tt class="py-line">    <tt class="py-name">model</tt> <tt class="py-op">=</tt> <tt class="py-name">dict</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">random</tt><tt class="py-op">.</tt><tt class="py-name">choice</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">True</tt><tt class="py-op">,</tt> <tt class="py-name">False</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt>  </tt>
<a name="L776"></a><tt class="py-lineno"> 776</tt>  <tt class="py-line">                 <tt class="py-keyword">for</tt> <tt class="py-name">s</tt> <tt class="py-keyword">in</tt> <tt id="link-255" class="py-name"><a title="spade.logic.prop_symbols" class="py-name" href="#" onclick="return doclink('link-255', 'prop_symbols', 'link-85');">prop_symbols</a></tt><tt class="py-op">(</tt><tt class="py-name">clauses</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L777"></a><tt class="py-lineno"> 777</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">max_flips</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L778"></a><tt class="py-lineno"> 778</tt>  <tt class="py-line">        <tt class="py-name">satisfied</tt><tt class="py-op">,</tt> <tt class="py-name">unsatisfied</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L779"></a><tt class="py-lineno"> 779</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">clause</tt> <tt class="py-keyword">in</tt> <tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L780"></a><tt class="py-lineno"> 780</tt>  <tt class="py-line">            <tt class="py-name">if_</tt><tt class="py-op">(</tt><tt id="link-256" class="py-name"><a title="spade.logic.pl_true" class="py-name" href="#" onclick="return doclink('link-256', 'pl_true', 'link-86');">pl_true</a></tt><tt class="py-op">(</tt><tt class="py-name">clause</tt><tt class="py-op">,</tt> <tt class="py-name">model</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">satisfied</tt><tt class="py-op">,</tt> <tt class="py-name">unsatisfied</tt><tt class="py-op">)</tt><tt class="py-op">.</tt><tt id="link-257" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-257', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt class="py-name">clause</tt><tt class="py-op">)</tt> </tt>
<a name="L781"></a><tt class="py-lineno"> 781</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">unsatisfied</tt><tt class="py-op">:</tt> <tt class="py-comment">## if model satisfies all the clauses</tt> </tt>
<a name="L782"></a><tt class="py-lineno"> 782</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">model</tt> </tt>
<a name="L783"></a><tt class="py-lineno"> 783</tt>  <tt class="py-line">        <tt class="py-name">clause</tt> <tt class="py-op">=</tt> <tt class="py-name">random</tt><tt class="py-op">.</tt><tt class="py-name">choice</tt><tt class="py-op">(</tt><tt class="py-name">unsatisfied</tt><tt class="py-op">)</tt> </tt>
<a name="L784"></a><tt class="py-lineno"> 784</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">probability</tt><tt class="py-op">(</tt><tt class="py-name">p</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L785"></a><tt class="py-lineno"> 785</tt>  <tt class="py-line">            <tt class="py-name">sym</tt> <tt class="py-op">=</tt> <tt class="py-name">random</tt><tt class="py-op">.</tt><tt class="py-name">choice</tt><tt class="py-op">(</tt><tt id="link-258" class="py-name"><a title="spade.logic.prop_symbols" class="py-name" href="#" onclick="return doclink('link-258', 'prop_symbols', 'link-85');">prop_symbols</a></tt><tt class="py-op">(</tt><tt class="py-name">clause</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L786"></a><tt class="py-lineno"> 786</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L787"></a><tt class="py-lineno"> 787</tt>  <tt class="py-line">            <tt class="py-comment">## Flip the symbol in clause that miximizes number of sat. clauses</tt> </tt>
<a name="L788"></a><tt class="py-lineno"> 788</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">NotImplementedError</tt> </tt>
<a name="L789"></a><tt class="py-lineno"> 789</tt>  <tt class="py-line">        <tt class="py-name">model</tt><tt class="py-op">[</tt><tt class="py-name">sym</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-keyword">not</tt> <tt class="py-name">model</tt><tt class="py-op">[</tt><tt class="py-name">sym</tt><tt class="py-op">]</tt> </tt>
<a name="L790"></a><tt class="py-lineno"> 790</tt>  <tt class="py-line"> </tt>
<a name="L791"></a><tt class="py-lineno"> 791</tt>  <tt class="py-line"> </tt>
<a name="L792"></a><tt class="py-lineno"> 792</tt>  <tt class="py-line"><tt class="py-comment"># PL-Wumpus-Agent [Fig. 7.19]</tt> </tt>
<a name="L793"></a><tt class="py-lineno"> 793</tt>  <tt class="py-line"><tt class="py-comment">#class PLWumpusAgent(agents.Agent):</tt> </tt>
<a name="L794"></a><tt class="py-lineno"> 794</tt>  <tt class="py-line">    <tt class="py-string">"""An agent for the wumpus world that does logical inference. [Fig. 7.19]"""</tt> </tt>
<a name="L795"></a><tt class="py-lineno"> 795</tt>  <tt class="py-line">    <tt class="py-string">"""def __init__(self):</tt> </tt>
<a name="L796"></a><tt class="py-lineno"> 796</tt>  <tt class="py-line"><tt class="py-string">        KB = FOLKB() ## shouldn't this be a propositional KB? ***</tt> </tt>
<a name="L797"></a><tt class="py-lineno"> 797</tt>  <tt class="py-line"><tt class="py-string">        x, y, orientation = 1, 1, (1, 0)</tt> </tt>
<a name="L798"></a><tt class="py-lineno"> 798</tt>  <tt class="py-line"><tt class="py-string">        visited = set() ## squares already visited</tt> </tt>
<a name="L799"></a><tt class="py-lineno"> 799</tt>  <tt class="py-line"><tt class="py-string">        action = None</tt> </tt>
<a name="L800"></a><tt class="py-lineno"> 800</tt>  <tt class="py-line"><tt class="py-string">        plan = []</tt> </tt>
<a name="L801"></a><tt class="py-lineno"> 801</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L802"></a><tt class="py-lineno"> 802</tt>  <tt class="py-line"><tt class="py-string">        def program(percept):</tt> </tt>
<a name="L803"></a><tt class="py-lineno"> 803</tt>  <tt class="py-line"><tt class="py-string">            stench, breeze, glitter = percept</tt> </tt>
<a name="L804"></a><tt class="py-lineno"> 804</tt>  <tt class="py-line"><tt class="py-string">            x, y, orientation = update_position(x, y, orientation, action)</tt> </tt>
<a name="L805"></a><tt class="py-lineno"> 805</tt>  <tt class="py-line"><tt class="py-string">            KB.tell('%sS_%d,%d' % (if_(stench, '', '~'), x, y))</tt> </tt>
<a name="L806"></a><tt class="py-lineno"> 806</tt>  <tt class="py-line"><tt class="py-string">            KB.tell('%sB_%d,%d' % (if_(breeze, '', '~'), x, y))</tt> </tt>
<a name="L807"></a><tt class="py-lineno"> 807</tt>  <tt class="py-line"><tt class="py-string">            if glitter: action = 'Grab'</tt> </tt>
<a name="L808"></a><tt class="py-lineno"> 808</tt>  <tt class="py-line"><tt class="py-string">            elif plan: action = plan.pop()</tt> </tt>
<a name="L809"></a><tt class="py-lineno"> 809</tt>  <tt class="py-line"><tt class="py-string">            else:</tt> </tt>
<a name="L810"></a><tt class="py-lineno"> 810</tt>  <tt class="py-line"><tt class="py-string">                for [i, j] in fringe(visited):</tt> </tt>
<a name="L811"></a><tt class="py-lineno"> 811</tt>  <tt class="py-line"><tt class="py-string">                    if KB.ask('~P_%d,%d &amp; ~W_%d,%d' % (i, j, i, j)) != False:</tt> </tt>
<a name="L812"></a><tt class="py-lineno"> 812</tt>  <tt class="py-line"><tt class="py-string">                        raise NotImplementedError</tt> </tt>
<a name="L813"></a><tt class="py-lineno"> 813</tt>  <tt class="py-line"><tt class="py-string">                    KB.ask('~P_%d,%d | ~W_%d,%d' % (i, j, i, j)) != False </tt> </tt>
<a name="L814"></a><tt class="py-lineno"> 814</tt>  <tt class="py-line"><tt class="py-string">            if action == None: </tt> </tt>
<a name="L815"></a><tt class="py-lineno"> 815</tt>  <tt class="py-line"><tt class="py-string">                action = random.choice(['Forward', 'Right', 'Left'])</tt> </tt>
<a name="L816"></a><tt class="py-lineno"> 816</tt>  <tt class="py-line"><tt class="py-string">            return action</tt> </tt>
<a name="L817"></a><tt class="py-lineno"> 817</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L818"></a><tt class="py-lineno"> 818</tt>  <tt class="py-line"><tt class="py-string">        self.program = program"""</tt> </tt>
</div><a name="L819"></a><tt class="py-lineno"> 819</tt>  <tt class="py-line"> </tt>
<a name="update_position"></a><div id="update_position-def"><a name="L820"></a><tt class="py-lineno"> 820</tt> <a class="py-toggle" href="#" id="update_position-toggle" onclick="return toggle('update_position');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#update_position">update_position</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">orientation</tt><tt class="py-op">,</tt> <tt class="py-param">action</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="update_position-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="update_position-expanded"><a name="L821"></a><tt class="py-lineno"> 821</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">action</tt> <tt class="py-op">==</tt> <tt class="py-string">'TurnRight'</tt><tt class="py-op">:</tt> </tt>
<a name="L822"></a><tt class="py-lineno"> 822</tt>  <tt class="py-line">        <tt class="py-name">orientation</tt> <tt class="py-op">=</tt> <tt class="py-name">turn_right</tt><tt class="py-op">(</tt><tt class="py-name">orientation</tt><tt class="py-op">)</tt> </tt>
<a name="L823"></a><tt class="py-lineno"> 823</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">action</tt> <tt class="py-op">==</tt> <tt class="py-string">'TurnLeft'</tt><tt class="py-op">:</tt> </tt>
<a name="L824"></a><tt class="py-lineno"> 824</tt>  <tt class="py-line">        <tt class="py-name">orientation</tt> <tt class="py-op">=</tt> <tt class="py-name">turn_left</tt><tt class="py-op">(</tt><tt class="py-name">orientation</tt><tt class="py-op">)</tt> </tt>
<a name="L825"></a><tt class="py-lineno"> 825</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">action</tt> <tt class="py-op">==</tt> <tt class="py-string">'Forward'</tt><tt class="py-op">:</tt> </tt>
<a name="L826"></a><tt class="py-lineno"> 826</tt>  <tt class="py-line">        <tt id="link-259" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-259', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-260" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-260', 'y', 'link-81');">y</a></tt> <tt class="py-op">=</tt> <tt id="link-261" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-261', 'x', 'link-0');">x</a></tt> <tt class="py-op">+</tt> <tt class="py-name">vector_add</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt id="link-262" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-262', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-263" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-263', 'y', 'link-81');">y</a></tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">orientation</tt><tt class="py-op">)</tt> </tt>
<a name="L827"></a><tt class="py-lineno"> 827</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-264" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-264', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-265" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-265', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt class="py-name">orientation</tt> </tt>
</div><a name="L828"></a><tt class="py-lineno"> 828</tt>  <tt class="py-line">     </tt>
<a name="L829"></a><tt class="py-lineno"> 829</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L830"></a><tt class="py-lineno"> 830</tt>  <tt class="py-line"> </tt>
<a name="unify"></a><div id="unify-def"><a name="L831"></a><tt class="py-lineno"> 831</tt> <a class="py-toggle" href="#" id="unify-toggle" onclick="return toggle('unify');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#unify">unify</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="unify-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="unify-expanded"><a name="L832"></a><tt class="py-lineno"> 832</tt>  <tt class="py-line">    <tt class="py-docstring">"""Unify expressions x,y with substitution s; return a substitution that</tt> </tt>
<a name="L833"></a><tt class="py-lineno"> 833</tt>  <tt class="py-line"><tt class="py-docstring">    would make x,y equal, or None if x,y can not unify. x and y can be</tt> </tt>
<a name="L834"></a><tt class="py-lineno"> 834</tt>  <tt class="py-line"><tt class="py-docstring">    variables (e.g. Expr('x')), constants, lists, or Exprs. [Fig. 9.1]</tt> </tt>
<a name="L835"></a><tt class="py-lineno"> 835</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppsubst(unify(x + y, y + C, {}))</tt> </tt>
<a name="L836"></a><tt class="py-lineno"> 836</tt>  <tt class="py-line"><tt class="py-docstring">    {x: y, y: C}</tt> </tt>
<a name="L837"></a><tt class="py-lineno"> 837</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L838"></a><tt class="py-lineno"> 838</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">s</tt> <tt class="py-op">==</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L839"></a><tt class="py-lineno"> 839</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
<a name="L840"></a><tt class="py-lineno"> 840</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-266" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-266', 'x', 'link-0');">x</a></tt> <tt class="py-op">==</tt> <tt id="link-267" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-267', 'y', 'link-81');">y</a></tt><tt class="py-op">:</tt> </tt>
<a name="L841"></a><tt class="py-lineno"> 841</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt> </tt>
<a name="L842"></a><tt class="py-lineno"> 842</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-268" class="py-name"><a title="spade.logic.is_variable" class="py-name" href="#" onclick="return doclink('link-268', 'is_variable', 'link-60');">is_variable</a></tt><tt class="py-op">(</tt><tt id="link-269" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-269', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L843"></a><tt class="py-lineno"> 843</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-270" class="py-name" targets="Function spade.logic.unify_var()=spade.logic-module.html#unify_var"><a title="spade.logic.unify_var" class="py-name" href="#" onclick="return doclink('link-270', 'unify_var', 'link-270');">unify_var</a></tt><tt class="py-op">(</tt><tt id="link-271" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-271', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-272" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-272', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L844"></a><tt class="py-lineno"> 844</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-273" class="py-name"><a title="spade.logic.is_variable" class="py-name" href="#" onclick="return doclink('link-273', 'is_variable', 'link-60');">is_variable</a></tt><tt class="py-op">(</tt><tt id="link-274" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-274', 'y', 'link-81');">y</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L845"></a><tt class="py-lineno"> 845</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-275" class="py-name"><a title="spade.logic.unify_var" class="py-name" href="#" onclick="return doclink('link-275', 'unify_var', 'link-270');">unify_var</a></tt><tt class="py-op">(</tt><tt id="link-276" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-276', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt id="link-277" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-277', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L846"></a><tt class="py-lineno"> 846</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-278" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-278', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-279" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-279', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-280" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-280', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt id="link-281" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-281', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L847"></a><tt class="py-lineno"> 847</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-282" class="py-name" targets="Function spade.logic.unify()=spade.logic-module.html#unify"><a title="spade.logic.unify" class="py-name" href="#" onclick="return doclink('link-282', 'unify', 'link-282');">unify</a></tt><tt class="py-op">(</tt><tt id="link-283" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-283', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">,</tt> <tt id="link-284" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-284', 'y', 'link-81');">y</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">,</tt> <tt id="link-285" class="py-name"><a title="spade.logic.unify" class="py-name" href="#" onclick="return doclink('link-285', 'unify', 'link-282');">unify</a></tt><tt class="py-op">(</tt><tt id="link-286" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-286', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt id="link-287" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-287', 'y', 'link-81');">y</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L848"></a><tt class="py-lineno"> 848</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-288" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-288', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">str</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-289" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-289', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt class="py-name">str</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> <tt class="py-keyword">not</tt> <tt id="link-290" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-290', 'x', 'link-0');">x</a></tt> <tt class="py-keyword">or</tt> <tt class="py-keyword">not</tt> <tt id="link-291" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-291', 'y', 'link-81');">y</a></tt><tt class="py-op">:</tt> </tt>
<a name="L849"></a><tt class="py-lineno"> 849</tt>  <tt class="py-line">        <tt class="py-comment"># orig. return if_(x == y, s, None) but we already know x != y</tt> </tt>
<a name="L850"></a><tt class="py-lineno"> 850</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
<a name="L851"></a><tt class="py-lineno"> 851</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-292" class="py-name" targets="Function spade.logic.issequence()=spade.logic-module.html#issequence"><a title="spade.logic.issequence" class="py-name" href="#" onclick="return doclink('link-292', 'issequence', 'link-292');">issequence</a></tt><tt class="py-op">(</tt><tt id="link-293" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-293', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt id="link-294" class="py-name"><a title="spade.logic.issequence" class="py-name" href="#" onclick="return doclink('link-294', 'issequence', 'link-292');">issequence</a></tt><tt class="py-op">(</tt><tt id="link-295" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-295', 'y', 'link-81');">y</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt id="link-296" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-296', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt id="link-297" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-297', 'y', 'link-81');">y</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L852"></a><tt class="py-lineno"> 852</tt>  <tt class="py-line">        <tt class="py-comment"># Assert neither x nor y is []</tt> </tt>
<a name="L853"></a><tt class="py-lineno"> 853</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-298" class="py-name"><a title="spade.logic.unify" class="py-name" href="#" onclick="return doclink('link-298', 'unify', 'link-282');">unify</a></tt><tt class="py-op">(</tt><tt id="link-299" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-299', 'x', 'link-0');">x</a></tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt id="link-300" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-300', 'y', 'link-81');">y</a></tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt id="link-301" class="py-name"><a title="spade.logic.unify" class="py-name" href="#" onclick="return doclink('link-301', 'unify', 'link-282');">unify</a></tt><tt class="py-op">(</tt><tt id="link-302" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-302', 'x', 'link-0');">x</a></tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt id="link-303" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-303', 'y', 'link-81');">y</a></tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L854"></a><tt class="py-lineno"> 854</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L855"></a><tt class="py-lineno"> 855</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
</div><a name="L856"></a><tt class="py-lineno"> 856</tt>  <tt class="py-line"> </tt>
<a name="is_variable"></a><div id="is_variable-def"><a name="L857"></a><tt class="py-lineno"> 857</tt> <a class="py-toggle" href="#" id="is_variable-toggle" onclick="return toggle('is_variable');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#is_variable">is_variable</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="is_variable-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="is_variable-expanded"><a name="L858"></a><tt class="py-lineno"> 858</tt>  <tt class="py-line">    <tt class="py-docstring">"A variable is an Expr with no args and a lowercase symbol as the op."</tt> </tt>
<a name="L859"></a><tt class="py-lineno"> 859</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-304" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-304', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-305" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-305', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-keyword">not</tt> <tt id="link-306" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-306', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt> <tt class="py-keyword">and</tt> <tt id="link-307" class="py-name" targets="Function spade.logic.is_var_symbol()=spade.logic-module.html#is_var_symbol"><a title="spade.logic.is_var_symbol" class="py-name" href="#" onclick="return doclink('link-307', 'is_var_symbol', 'link-307');">is_var_symbol</a></tt><tt class="py-op">(</tt><tt id="link-308" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-308', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt> </tt>
</div><a name="L860"></a><tt class="py-lineno"> 860</tt>  <tt class="py-line"> </tt>
<a name="unify_var"></a><div id="unify_var-def"><a name="L861"></a><tt class="py-lineno"> 861</tt> <a class="py-toggle" href="#" id="unify_var-toggle" onclick="return toggle('unify_var');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#unify_var">unify_var</a><tt class="py-op">(</tt><tt class="py-param">var</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="unify_var-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="unify_var-expanded"><a name="L862"></a><tt class="py-lineno"> 862</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">var</tt> <tt class="py-keyword">in</tt> <tt class="py-name">s</tt><tt class="py-op">:</tt> </tt>
<a name="L863"></a><tt class="py-lineno"> 863</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-309" class="py-name"><a title="spade.logic.unify" class="py-name" href="#" onclick="return doclink('link-309', 'unify', 'link-282');">unify</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">[</tt><tt class="py-name">var</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt id="link-310" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-310', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L864"></a><tt class="py-lineno"> 864</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-311" class="py-name" targets="Function spade.logic.occur_check()=spade.logic-module.html#occur_check"><a title="spade.logic.occur_check" class="py-name" href="#" onclick="return doclink('link-311', 'occur_check', 'link-311');">occur_check</a></tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">,</tt> <tt id="link-312" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-312', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L865"></a><tt class="py-lineno"> 865</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">None</tt> </tt>
<a name="L866"></a><tt class="py-lineno"> 866</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L867"></a><tt class="py-lineno"> 867</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-313" class="py-name"><a title="spade.logic.extend" class="py-name" href="#" onclick="return doclink('link-313', 'extend', 'link-12');">extend</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">var</tt><tt class="py-op">,</tt> <tt id="link-314" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-314', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L868"></a><tt class="py-lineno"> 868</tt>  <tt class="py-line"> </tt>
<a name="occur_check"></a><div id="occur_check-def"><a name="L869"></a><tt class="py-lineno"> 869</tt> <a class="py-toggle" href="#" id="occur_check-toggle" onclick="return toggle('occur_check');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#occur_check">occur_check</a><tt class="py-op">(</tt><tt class="py-param">var</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="occur_check-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="occur_check-expanded"><a name="L870"></a><tt class="py-lineno"> 870</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return true if variable var occurs anywhere in x</tt> </tt>
<a name="L871"></a><tt class="py-lineno"> 871</tt>  <tt class="py-line"><tt class="py-docstring">    (or in subst(s, x), if s has a binding for x)."""</tt> </tt>
<a name="L872"></a><tt class="py-lineno"> 872</tt>  <tt class="py-line"> </tt>
<a name="L873"></a><tt class="py-lineno"> 873</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">var</tt> <tt class="py-op">==</tt> <tt id="link-315" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-315', 'x', 'link-0');">x</a></tt><tt class="py-op">:</tt> </tt>
<a name="L874"></a><tt class="py-lineno"> 874</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">True</tt> </tt>
<a name="L875"></a><tt class="py-lineno"> 875</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-316" class="py-name"><a title="spade.logic.is_variable" class="py-name" href="#" onclick="return doclink('link-316', 'is_variable', 'link-60');">is_variable</a></tt><tt class="py-op">(</tt><tt id="link-317" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-317', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt class="py-name">has_key</tt><tt class="py-op">(</tt><tt id="link-318" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-318', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L876"></a><tt class="py-lineno"> 876</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-319" class="py-name"><a title="spade.logic.occur_check" class="py-name" href="#" onclick="return doclink('link-319', 'occur_check', 'link-311');">occur_check</a></tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">[</tt><tt id="link-320" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-320', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-comment"># fixed</tt> </tt>
<a name="L877"></a><tt class="py-lineno"> 877</tt>  <tt class="py-line">    <tt class="py-comment"># What else might x be?  an Expr, a list, a string?</tt> </tt>
<a name="L878"></a><tt class="py-lineno"> 878</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-321" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-321', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-322" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-322', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L879"></a><tt class="py-lineno"> 879</tt>  <tt class="py-line">        <tt class="py-comment"># Compare operator and arguments</tt> </tt>
<a name="L880"></a><tt class="py-lineno"> 880</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-323" class="py-name"><a title="spade.logic.occur_check" class="py-name" href="#" onclick="return doclink('link-323', 'occur_check', 'link-311');">occur_check</a></tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">,</tt> <tt id="link-324" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-324', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> </tt>
<a name="L881"></a><tt class="py-lineno"> 881</tt>  <tt class="py-line">                <tt id="link-325" class="py-name"><a title="spade.logic.occur_check" class="py-name" href="#" onclick="return doclink('link-325', 'occur_check', 'link-311');">occur_check</a></tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">,</tt> <tt id="link-326" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-326', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L882"></a><tt class="py-lineno"> 882</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-327" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-327', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">list</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt id="link-328" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-328', 'x', 'link-0');">x</a></tt> <tt class="py-op">!=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">:</tt> </tt>
<a name="L883"></a><tt class="py-lineno"> 883</tt>  <tt class="py-line">        <tt class="py-comment"># Compare first and rest</tt> </tt>
<a name="L884"></a><tt class="py-lineno"> 884</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt id="link-329" class="py-name"><a title="spade.logic.occur_check" class="py-name" href="#" onclick="return doclink('link-329', 'occur_check', 'link-311');">occur_check</a></tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">,</tt> <tt id="link-330" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-330', 'x', 'link-0');">x</a></tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt> <tt class="py-keyword">or</tt> </tt>
<a name="L885"></a><tt class="py-lineno"> 885</tt>  <tt class="py-line">                <tt id="link-331" class="py-name"><a title="spade.logic.occur_check" class="py-name" href="#" onclick="return doclink('link-331', 'occur_check', 'link-311');">occur_check</a></tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">,</tt> <tt id="link-332" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-332', 'x', 'link-0');">x</a></tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">s</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L886"></a><tt class="py-lineno"> 886</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L887"></a><tt class="py-lineno"> 887</tt>  <tt class="py-line">        <tt class="py-comment"># A variable cannot occur in a string</tt> </tt>
<a name="L888"></a><tt class="py-lineno"> 888</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">False</tt> </tt>
</div><a name="L889"></a><tt class="py-lineno"> 889</tt>  <tt class="py-line">     </tt>
<a name="L890"></a><tt class="py-lineno"> 890</tt>  <tt class="py-line">    <tt class="py-comment">#elif isinstance(x, Expr):</tt> </tt>
<a name="L891"></a><tt class="py-lineno"> 891</tt>  <tt class="py-line">    <tt class="py-comment">#    return var.op == x.op or occur_check(var, x.args)</tt> </tt>
<a name="L892"></a><tt class="py-lineno"> 892</tt>  <tt class="py-line">    <tt class="py-comment">#elif not isinstance(x, str) and issequence(x):</tt> </tt>
<a name="L893"></a><tt class="py-lineno"> 893</tt>  <tt class="py-line">    <tt class="py-comment">#    for xi in x:</tt> </tt>
<a name="L894"></a><tt class="py-lineno"> 894</tt>  <tt class="py-line">    <tt class="py-comment">#        if occur_check(var, xi): return True</tt> </tt>
<a name="L895"></a><tt class="py-lineno"> 895</tt>  <tt class="py-line">    <tt class="py-comment">#return False</tt> </tt>
<a name="L896"></a><tt class="py-lineno"> 896</tt>  <tt class="py-line"> </tt>
<a name="extend"></a><div id="extend-def"><a name="L897"></a><tt class="py-lineno"> 897</tt> <a class="py-toggle" href="#" id="extend-toggle" onclick="return toggle('extend');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#extend">extend</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">,</tt> <tt class="py-param">var</tt><tt class="py-op">,</tt> <tt class="py-param">val</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="extend-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="extend-expanded"><a name="L898"></a><tt class="py-lineno"> 898</tt>  <tt class="py-line">    <tt class="py-docstring">"""Copy the substitution s and extend it by setting var to val;</tt> </tt>
<a name="L899"></a><tt class="py-lineno"> 899</tt>  <tt class="py-line"><tt class="py-docstring">    return copy.</tt> </tt>
<a name="L900"></a><tt class="py-lineno"> 900</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L901"></a><tt class="py-lineno"> 901</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppsubst(extend({x: 1}, y, 2))</tt> </tt>
<a name="L902"></a><tt class="py-lineno"> 902</tt>  <tt class="py-line"><tt class="py-docstring">    {x: 1, y: 2}</tt> </tt>
<a name="L903"></a><tt class="py-lineno"> 903</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L904"></a><tt class="py-lineno"> 904</tt>  <tt class="py-line">    <tt class="py-name">s2</tt> <tt class="py-op">=</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt id="link-333" class="py-name" targets="Method spade.pyparsing.Keyword.copy()=spade.pyparsing.Keyword-class.html#copy,Method spade.pyparsing.ParseResults.copy()=spade.pyparsing.ParseResults-class.html#copy,Method spade.pyparsing.ParserElement.copy()=spade.pyparsing.ParserElement-class.html#copy"><a title="spade.pyparsing.Keyword.copy
spade.pyparsing.ParseResults.copy
spade.pyparsing.ParserElement.copy" class="py-name" href="#" onclick="return doclink('link-333', 'copy', 'link-333');">copy</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L905"></a><tt class="py-lineno"> 905</tt>  <tt class="py-line">    <tt class="py-name">s2</tt><tt class="py-op">[</tt><tt class="py-name">var</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">val</tt> </tt>
<a name="L906"></a><tt class="py-lineno"> 906</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">s2</tt> </tt>
</div><a name="L907"></a><tt class="py-lineno"> 907</tt>  <tt class="py-line">     </tt>
<a name="subst"></a><div id="subst-def"><a name="L908"></a><tt class="py-lineno"> 908</tt> <a class="py-toggle" href="#" id="subst-toggle" onclick="return toggle('subst');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#subst">subst</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="subst-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="subst-expanded"><a name="L909"></a><tt class="py-lineno"> 909</tt>  <tt class="py-line">    <tt class="py-docstring">"""Substitute the substitution s into the expression x.</tt> </tt>
<a name="L910"></a><tt class="py-lineno"> 910</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst({x: 42, y:0}, F(x) + y)</tt> </tt>
<a name="L911"></a><tt class="py-lineno"> 911</tt>  <tt class="py-line"><tt class="py-docstring">    (F(42) + 0)</tt> </tt>
<a name="L912"></a><tt class="py-lineno"> 912</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L913"></a><tt class="py-lineno"> 913</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-334" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-334', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">list</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
<a name="L914"></a><tt class="py-lineno"> 914</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-op">[</tt><tt id="link-335" class="py-name" targets="Function spade.logic.subst()=spade.logic-module.html#subst"><a title="spade.logic.subst" class="py-name" href="#" onclick="return doclink('link-335', 'subst', 'link-335');">subst</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">xi</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">xi</tt> <tt class="py-keyword">in</tt> <tt id="link-336" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-336', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt> </tt>
<a name="L915"></a><tt class="py-lineno"> 915</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-337" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-337', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">tuple</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
<a name="L916"></a><tt class="py-lineno"> 916</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">tuple</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt id="link-338" class="py-name"><a title="spade.logic.subst" class="py-name" href="#" onclick="return doclink('link-338', 'subst', 'link-335');">subst</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">xi</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">xi</tt> <tt class="py-keyword">in</tt> <tt id="link-339" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-339', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L917"></a><tt class="py-lineno"> 917</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-keyword">not</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt id="link-340" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-340', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-341" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-341', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
<a name="L918"></a><tt class="py-lineno"> 918</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-342" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-342', 'x', 'link-0');">x</a></tt> </tt>
<a name="L919"></a><tt class="py-lineno"> 919</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-343" class="py-name"><a title="spade.logic.is_var_symbol" class="py-name" href="#" onclick="return doclink('link-343', 'is_var_symbol', 'link-307');">is_var_symbol</a></tt><tt class="py-op">(</tt><tt id="link-344" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-344', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
<a name="L920"></a><tt class="py-lineno"> 920</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">s</tt><tt class="py-op">.</tt><tt id="link-345" class="py-name"><a title="spade.xmppd.modules.db_fake.DB.get" class="py-name" href="#" onclick="return doclink('link-345', 'get', 'link-108');">get</a></tt><tt class="py-op">(</tt><tt id="link-346" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-346', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt id="link-347" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-347', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L921"></a><tt class="py-lineno"> 921</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt>  </tt>
<a name="L922"></a><tt class="py-lineno"> 922</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-348" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-348', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt id="link-349" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-349', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-op">[</tt><tt id="link-350" class="py-name"><a title="spade.logic.subst" class="py-name" href="#" onclick="return doclink('link-350', 'subst', 'link-335');">subst</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">,</tt> <tt class="py-name">arg</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">arg</tt> <tt class="py-keyword">in</tt> <tt id="link-351" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-351', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="L923"></a><tt class="py-lineno"> 923</tt>  <tt class="py-line">         </tt>
<a name="fol_fc_ask"></a><div id="fol_fc_ask-def"><a name="L924"></a><tt class="py-lineno"> 924</tt> <a class="py-toggle" href="#" id="fol_fc_ask-toggle" onclick="return toggle('fol_fc_ask');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#fol_fc_ask">fol_fc_ask</a><tt class="py-op">(</tt><tt class="py-param">KB</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="fol_fc_ask-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="fol_fc_ask-expanded"><a name="L925"></a><tt class="py-lineno"> 925</tt>  <tt class="py-line">    <tt class="py-docstring">"""Inefficient forward chaining for first-order logic. [Fig. 9.3]</tt> </tt>
<a name="L926"></a><tt class="py-lineno"> 926</tt>  <tt class="py-line"><tt class="py-docstring">    KB is an FOLHornKB and alpha must be an atomic sentence."""</tt> </tt>
<a name="L927"></a><tt class="py-lineno"> 927</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">True</tt><tt class="py-op">:</tt> </tt>
<a name="L928"></a><tt class="py-lineno"> 928</tt>  <tt class="py-line">        <tt class="py-name">new</tt> <tt class="py-op">=</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
<a name="L929"></a><tt class="py-lineno"> 929</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">r</tt> <tt class="py-keyword">in</tt> <tt id="link-352" class="py-name"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-352', 'KB', 'link-169');">KB</a></tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L930"></a><tt class="py-lineno"> 930</tt>  <tt class="py-line">            <tt class="py-name">r1</tt> <tt class="py-op">=</tt> <tt id="link-353" class="py-name" targets="Function spade.logic.standardize_apart()=spade.logic-module.html#standardize_apart"><a title="spade.logic.standardize_apart" class="py-name" href="#" onclick="return doclink('link-353', 'standardize_apart', 'link-353');">standardize_apart</a></tt><tt class="py-op">(</tt><tt class="py-name">r</tt><tt class="py-op">)</tt> </tt>
<a name="L931"></a><tt class="py-lineno"> 931</tt>  <tt class="py-line">            <tt class="py-name">ps</tt><tt class="py-op">,</tt> <tt class="py-name">q</tt> <tt class="py-op">=</tt> <tt id="link-354" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-354', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt class="py-name">r</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">r</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L932"></a><tt class="py-lineno"> 932</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">NotImplementedError</tt> </tt>
</div><a name="L933"></a><tt class="py-lineno"> 933</tt>  <tt class="py-line"> </tt>
<a name="standardize_apart"></a><div id="standardize_apart-def"><a name="L934"></a><tt class="py-lineno"> 934</tt> <a class="py-toggle" href="#" id="standardize_apart-toggle" onclick="return toggle('standardize_apart');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#standardize_apart">standardize_apart</a><tt class="py-op">(</tt><tt class="py-param">sentence</tt><tt class="py-op">,</tt> <tt class="py-param">dic</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="standardize_apart-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="standardize_apart-expanded"><a name="L935"></a><tt class="py-lineno"> 935</tt>  <tt class="py-line">    <tt class="py-docstring">"""Replace all the variables in sentence with new variables.</tt> </tt>
<a name="L936"></a><tt class="py-lineno"> 936</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; e = expr('F(a, b, c) &amp; G(c, A, 23)')</tt> </tt>
<a name="L937"></a><tt class="py-lineno"> 937</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; len(variables(standardize_apart(e)))</tt> </tt>
<a name="L938"></a><tt class="py-lineno"> 938</tt>  <tt class="py-line"><tt class="py-docstring">    3</tt> </tt>
<a name="L939"></a><tt class="py-lineno"> 939</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; variables(e).intersection(variables(standardize_apart(e)))</tt> </tt>
<a name="L940"></a><tt class="py-lineno"> 940</tt>  <tt class="py-line"><tt class="py-docstring">    set([])</tt> </tt>
<a name="L941"></a><tt class="py-lineno"> 941</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; is_variable(standardize_apart(expr('x')))</tt> </tt>
<a name="L942"></a><tt class="py-lineno"> 942</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L943"></a><tt class="py-lineno"> 943</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L944"></a><tt class="py-lineno"> 944</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">isinstance</tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">,</tt> <tt id="link-355" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-355', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L945"></a><tt class="py-lineno"> 945</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">sentence</tt> </tt>
<a name="L946"></a><tt class="py-lineno"> 946</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt id="link-356" class="py-name"><a title="spade.logic.is_var_symbol" class="py-name" href="#" onclick="return doclink('link-356', 'is_var_symbol', 'link-307');">is_var_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
<a name="L947"></a><tt class="py-lineno"> 947</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">sentence</tt> <tt class="py-keyword">in</tt> <tt class="py-name">dic</tt><tt class="py-op">:</tt> </tt>
<a name="L948"></a><tt class="py-lineno"> 948</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">dic</tt><tt class="py-op">[</tt><tt class="py-name">sentence</tt><tt class="py-op">]</tt> </tt>
<a name="L949"></a><tt class="py-lineno"> 949</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L950"></a><tt class="py-lineno"> 950</tt>  <tt class="py-line">            <tt id="link-357" class="py-name"><a title="spade.logic.standardize_apart" class="py-name" href="#" onclick="return doclink('link-357', 'standardize_apart', 'link-353');">standardize_apart</a></tt><tt class="py-op">.</tt><tt class="py-name">counter</tt> <tt class="py-op">+=</tt> <tt class="py-number">1</tt> </tt>
<a name="L951"></a><tt class="py-lineno"> 951</tt>  <tt class="py-line">            <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt id="link-358" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-358', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'v_%d'</tt> <tt class="py-op">%</tt> <tt id="link-359" class="py-name"><a title="spade.logic.standardize_apart" class="py-name" href="#" onclick="return doclink('link-359', 'standardize_apart', 'link-353');">standardize_apart</a></tt><tt class="py-op">.</tt><tt class="py-name">counter</tt><tt class="py-op">)</tt> </tt>
<a name="L952"></a><tt class="py-lineno"> 952</tt>  <tt class="py-line">            <tt class="py-name">dic</tt><tt class="py-op">[</tt><tt class="py-name">sentence</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">v</tt> </tt>
<a name="L953"></a><tt class="py-lineno"> 953</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-name">v</tt> </tt>
<a name="L954"></a><tt class="py-lineno"> 954</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt>  </tt>
<a name="L955"></a><tt class="py-lineno"> 955</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-360" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-360', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> </tt>
<a name="L956"></a><tt class="py-lineno"> 956</tt>  <tt class="py-line">                    <tt class="py-op">*</tt><tt class="py-op">[</tt><tt id="link-361" class="py-name"><a title="spade.logic.standardize_apart" class="py-name" href="#" onclick="return doclink('link-361', 'standardize_apart', 'link-353');">standardize_apart</a></tt><tt class="py-op">(</tt><tt id="link-362" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-362', 'a', 'link-122');">a</a></tt><tt class="py-op">,</tt> <tt class="py-name">dic</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt id="link-363" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-363', 'a', 'link-122');">a</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">sentence</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="L957"></a><tt class="py-lineno"> 957</tt>  <tt class="py-line"> </tt>
<a name="L958"></a><tt class="py-lineno"> 958</tt>  <tt class="py-line"><tt id="link-364" class="py-name"><a title="spade.logic.standardize_apart" class="py-name" href="#" onclick="return doclink('link-364', 'standardize_apart', 'link-353');">standardize_apart</a></tt><tt class="py-op">.</tt><tt class="py-name">counter</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L959"></a><tt class="py-lineno"> 959</tt>  <tt class="py-line"> </tt>
<a name="L960"></a><tt class="py-lineno"> 960</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L961"></a><tt class="py-lineno"> 961</tt>  <tt class="py-line"> </tt>
<a name="L962"></a><tt class="py-lineno"> 962</tt>  <tt class="py-line"> </tt>
<a name="FolKB"></a><div id="FolKB-def"><a name="L963"></a><tt class="py-lineno"> 963</tt> <a class="py-toggle" href="#" id="FolKB-toggle" onclick="return toggle('FolKB');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="spade.logic.FolKB-class.html">FolKB</a> <tt class="py-op">(</tt><tt class="py-base-class">KB</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="FolKB-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="FolKB-expanded"><a name="L964"></a><tt class="py-lineno"> 964</tt>  <tt class="py-line">    <tt class="py-docstring">"""A knowledge base consisting of first-order definite clauses</tt> </tt>
<a name="L965"></a><tt class="py-lineno"> 965</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; kb0 = FolKB([expr('Farmer(Mac)'), expr('Rabbit(Pete)'),</tt> </tt>
<a name="L966"></a><tt class="py-lineno"> 966</tt>  <tt class="py-line"><tt class="py-docstring">    ...              expr('(Rabbit(r) &amp; Farmer(f)) ==&gt; Hates(f, r)')])</tt> </tt>
<a name="L967"></a><tt class="py-lineno"> 967</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; kb0.tell(expr('Rabbit(Flopsie)'))</tt> </tt>
<a name="L968"></a><tt class="py-lineno"> 968</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; kb0.retract(expr('Rabbit(Pete)'))</tt> </tt>
<a name="L969"></a><tt class="py-lineno"> 969</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; kb0.ask(expr('Hates(Mac, x)'))[x]</tt> </tt>
<a name="L970"></a><tt class="py-lineno"> 970</tt>  <tt class="py-line"><tt class="py-docstring">    Flopsie</tt> </tt>
<a name="L971"></a><tt class="py-lineno"> 971</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; kb0.ask(expr('Wife(Pete, x)'))</tt> </tt>
<a name="L972"></a><tt class="py-lineno"> 972</tt>  <tt class="py-line"><tt class="py-docstring">    False</tt> </tt>
<a name="L973"></a><tt class="py-lineno"> 973</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L974"></a><tt class="py-lineno"> 974</tt>  <tt class="py-line"> </tt>
<a name="FolKB.__init__"></a><div id="FolKB.__init__-def"><a name="L975"></a><tt class="py-lineno"> 975</tt> <a class="py-toggle" href="#" id="FolKB.__init__-toggle" onclick="return toggle('FolKB.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.FolKB-class.html#__init__">__init__</a> <tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">initial_clauses</tt><tt class="py-op">=</tt><tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="FolKB.__init__-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="FolKB.__init__-expanded"><a name="L976"></a><tt class="py-lineno"> 976</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> <tt class="py-comment"># inefficient: no indexing</tt> </tt>
<a name="L977"></a><tt class="py-lineno"> 977</tt>  <tt class="py-line">        <tt class="py-keyword">for</tt> <tt class="py-name">clause</tt> <tt class="py-keyword">in</tt> <tt class="py-name">initial_clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L978"></a><tt class="py-lineno"> 978</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-365" class="py-name"><a title="spade.logic.FolKB.tell
spade.logic.KB.tell
spade.logic.PropHornKB.tell
spade.logic.PropKB.tell" class="py-name" href="#" onclick="return doclink('link-365', 'tell', 'link-11');">tell</a></tt><tt class="py-op">(</tt><tt class="py-name">clause</tt><tt class="py-op">)</tt> </tt>
</div><a name="L979"></a><tt class="py-lineno"> 979</tt>  <tt class="py-line"> </tt>
<a name="FolKB.tell"></a><div id="FolKB.tell-def"><a name="L980"></a><tt class="py-lineno"> 980</tt> <a class="py-toggle" href="#" id="FolKB.tell-toggle" onclick="return toggle('FolKB.tell');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.FolKB-class.html#tell">tell</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="FolKB.tell-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="FolKB.tell-expanded"><a name="L981"></a><tt class="py-lineno"> 981</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt id="link-366" class="py-name" targets="Function spade.logic.is_definite_clause()=spade.logic-module.html#is_definite_clause"><a title="spade.logic.is_definite_clause" class="py-name" href="#" onclick="return doclink('link-366', 'is_definite_clause', 'link-366');">is_definite_clause</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L982"></a><tt class="py-lineno"> 982</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt id="link-367" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-367', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt> </tt>
<a name="L983"></a><tt class="py-lineno"> 983</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L984"></a><tt class="py-lineno"> 984</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">Exception</tt><tt class="py-op">(</tt><tt class="py-string">"Not a definite clause: %s"</tt> <tt class="py-op">%</tt> <tt class="py-name">sentence</tt><tt class="py-op">)</tt> </tt>
</div><a name="L985"></a><tt class="py-lineno"> 985</tt>  <tt class="py-line"> </tt>
<a name="FolKB.ask_generator"></a><div id="FolKB.ask_generator-def"><a name="L986"></a><tt class="py-lineno"> 986</tt> <a class="py-toggle" href="#" id="FolKB.ask_generator-toggle" onclick="return toggle('FolKB.ask_generator');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.FolKB-class.html#ask_generator">ask_generator</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">query</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="FolKB.ask_generator-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="FolKB.ask_generator-expanded"><a name="L987"></a><tt class="py-lineno"> 987</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-368" class="py-name" targets="Function spade.logic.fol_bc_ask()=spade.logic-module.html#fol_bc_ask"><a title="spade.logic.fol_bc_ask" class="py-name" href="#" onclick="return doclink('link-368', 'fol_bc_ask', 'link-368');">fol_bc_ask</a></tt><tt class="py-op">(</tt><tt class="py-name">self</tt><tt class="py-op">,</tt> <tt class="py-op">[</tt><tt class="py-name">query</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="L988"></a><tt class="py-lineno"> 988</tt>  <tt class="py-line"> </tt>
<a name="FolKB.retract"></a><div id="FolKB.retract-def"><a name="L989"></a><tt class="py-lineno"> 989</tt> <a class="py-toggle" href="#" id="FolKB.retract-toggle" onclick="return toggle('FolKB.retract');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic.FolKB-class.html#retract">retract</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">sentence</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="FolKB.retract-collapsed" style="display:none;" pad="++++" indent="++++++++"></div><div id="FolKB.retract-expanded"><a name="L990"></a><tt class="py-lineno"> 990</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">.</tt><tt class="py-name">remove</tt><tt class="py-op">(</tt><tt class="py-name">sentence</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L991"></a><tt class="py-lineno"> 991</tt>  <tt class="py-line"> </tt>
<a name="test_ask"></a><div id="test_ask-def"><a name="L992"></a><tt class="py-lineno"> 992</tt> <a class="py-toggle" href="#" id="test_ask-toggle" onclick="return toggle('test_ask');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#test_ask">test_ask</a><tt class="py-op">(</tt><tt class="py-param">q</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="test_ask-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="test_ask-expanded"><a name="L993"></a><tt class="py-lineno"> 993</tt>  <tt class="py-line">    <tt id="link-369" class="py-name" targets="Variable spade.xmppd.xmppd.e=spade.xmppd.xmppd-module.html#e"><a title="spade.xmppd.xmppd.e" class="py-name" href="#" onclick="return doclink('link-369', 'e', 'link-369');">e</a></tt> <tt class="py-op">=</tt> <tt id="link-370" class="py-name"><a title="spade.logic.expr" class="py-name" href="#" onclick="return doclink('link-370', 'expr', 'link-24');">expr</a></tt><tt class="py-op">(</tt><tt class="py-name">q</tt><tt class="py-op">)</tt> </tt>
<a name="L994"></a><tt class="py-lineno"> 994</tt>  <tt class="py-line">    <tt class="py-name">vars</tt> <tt class="py-op">=</tt> <tt id="link-371" class="py-name"><a title="spade.logic.variables" class="py-name" href="#" onclick="return doclink('link-371', 'variables', 'link-62');">variables</a></tt><tt class="py-op">(</tt><tt id="link-372" class="py-name"><a title="spade.xmppd.xmppd.e" class="py-name" href="#" onclick="return doclink('link-372', 'e', 'link-369');">e</a></tt><tt class="py-op">)</tt> </tt>
<a name="L995"></a><tt class="py-lineno"> 995</tt>  <tt class="py-line">    <tt class="py-name">ans</tt> <tt class="py-op">=</tt> <tt id="link-373" class="py-name"><a title="spade.logic.fol_bc_ask" class="py-name" href="#" onclick="return doclink('link-373', 'fol_bc_ask', 'link-368');">fol_bc_ask</a></tt><tt class="py-op">(</tt><tt id="link-374" class="py-name" targets="Variable spade.bdi.test_kb=spade.bdi-module.html#test_kb,Variable spade.logic.test_kb=spade.logic-module.html#test_kb"><a title="spade.bdi.test_kb
spade.logic.test_kb" class="py-name" href="#" onclick="return doclink('link-374', 'test_kb', 'link-374');">test_kb</a></tt><tt class="py-op">,</tt> <tt class="py-op">[</tt><tt id="link-375" class="py-name"><a title="spade.xmppd.xmppd.e" class="py-name" href="#" onclick="return doclink('link-375', 'e', 'link-369');">e</a></tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L996"></a><tt class="py-lineno"> 996</tt>  <tt class="py-line">    <tt class="py-name">res</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L997"></a><tt class="py-lineno"> 997</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt id="link-376" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-376', 'a', 'link-122');">a</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">ans</tt><tt class="py-op">:</tt> </tt>
<a name="L998"></a><tt class="py-lineno"> 998</tt>  <tt class="py-line">        <tt class="py-name">res</tt><tt class="py-op">.</tt><tt id="link-377" class="py-name"><a title="spade.pyparsing.ParseExpression.append" class="py-name" href="#" onclick="return doclink('link-377', 'append', 'link-164');">append</a></tt><tt class="py-op">(</tt><tt id="link-378" class="py-name" targets="Function spade.logic.pretty()=spade.logic-module.html#pretty"><a title="spade.logic.pretty" class="py-name" href="#" onclick="return doclink('link-378', 'pretty', 'link-378');">pretty</a></tt><tt class="py-op">(</tt><tt class="py-name">dict</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-op">(</tt><tt id="link-379" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-379', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">v</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-op">(</tt><tt id="link-380" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-380', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">v</tt><tt class="py-op">)</tt> <tt class="py-keyword">in</tt> <tt id="link-381" class="py-name"><a title="spade.ACLMessage.ACLMessage.a" class="py-name" href="#" onclick="return doclink('link-381', 'a', 'link-122');">a</a></tt><tt class="py-op">.</tt><tt id="link-382" class="py-name" targets="Method spade.pyparsing.ParseResults.items()=spade.pyparsing.ParseResults-class.html#items"><a title="spade.pyparsing.ParseResults.items" class="py-name" href="#" onclick="return doclink('link-382', 'items', 'link-382');">items</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> <tt class="py-keyword">if</tt> <tt id="link-383" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-383', 'x', 'link-0');">x</a></tt> <tt class="py-keyword">in</tt> <tt class="py-name">vars</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L999"></a><tt class="py-lineno"> 999</tt>  <tt class="py-line">    <tt class="py-name">res</tt><tt class="py-op">.</tt><tt class="py-name">sort</tt><tt class="py-op">(</tt><tt class="py-name">key</tt><tt class="py-op">=</tt><tt class="py-name">str</tt><tt class="py-op">)</tt> </tt>
<a name="L1000"></a><tt class="py-lineno">1000</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">res</tt> </tt>
</div><a name="L1001"></a><tt class="py-lineno">1001</tt>  <tt class="py-line"> </tt>
<a name="L1002"></a><tt class="py-lineno">1002</tt>  <tt class="py-line"><tt id="link-384" class="py-name"><a title="spade.bdi.test_kb
spade.logic.test_kb" class="py-name" href="#" onclick="return doclink('link-384', 'test_kb', 'link-374');">test_kb</a></tt> <tt class="py-op">=</tt> <tt id="link-385" class="py-name" targets="Class spade.logic.FolKB=spade.logic.FolKB-class.html"><a title="spade.logic.FolKB" class="py-name" href="#" onclick="return doclink('link-385', 'FolKB', 'link-385');">FolKB</a></tt><tt class="py-op">(</tt> </tt>
<a name="L1003"></a><tt class="py-lineno">1003</tt>  <tt class="py-line">    <tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-386" class="py-name"><a title="spade.logic.expr" class="py-name" href="#" onclick="return doclink('link-386', 'expr', 'link-24');">expr</a></tt><tt class="py-op">,</tt> <tt class="py-op">[</tt><tt class="py-string">'Farmer(Mac)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1004"></a><tt class="py-lineno">1004</tt>  <tt class="py-line">               <tt class="py-string">'Rabbit(Pete)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1005"></a><tt class="py-lineno">1005</tt>  <tt class="py-line">               <tt class="py-string">'Mother(MrsMac, Mac)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1006"></a><tt class="py-lineno">1006</tt>  <tt class="py-line">               <tt class="py-string">'Mother(MrsRabbit, Pete)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1007"></a><tt class="py-lineno">1007</tt>  <tt class="py-line">               <tt class="py-string">'(Rabbit(r) &amp; Farmer(f)) ==&gt; Hates(f, r)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1008"></a><tt class="py-lineno">1008</tt>  <tt class="py-line">               <tt class="py-string">'(Mother(m, c)) ==&gt; Loves(m, c)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1009"></a><tt class="py-lineno">1009</tt>  <tt class="py-line">               <tt class="py-string">'(Mother(m, r) &amp; Rabbit(r)) ==&gt; Rabbit(m)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1010"></a><tt class="py-lineno">1010</tt>  <tt class="py-line">               <tt class="py-string">'(Farmer(f)) ==&gt; Human(f)'</tt><tt class="py-op">,</tt> </tt>
<a name="L1011"></a><tt class="py-lineno">1011</tt>  <tt class="py-line">               <tt class="py-comment"># Note that this order of conjuncts </tt> </tt>
<a name="L1012"></a><tt class="py-lineno">1012</tt>  <tt class="py-line">               <tt class="py-comment"># would result in infinite recursion:</tt> </tt>
<a name="L1013"></a><tt class="py-lineno">1013</tt>  <tt class="py-line">               <tt class="py-comment">#'(Human(h) &amp; Mother(m, h)) ==&gt; Human(m)'</tt> </tt>
<a name="L1014"></a><tt class="py-lineno">1014</tt>  <tt class="py-line">               <tt class="py-string">'(Mother(m, h) &amp; Human(h)) ==&gt; Human(m)'</tt> </tt>
<a name="L1015"></a><tt class="py-lineno">1015</tt>  <tt class="py-line">               <tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L1016"></a><tt class="py-lineno">1016</tt>  <tt class="py-line"><tt class="py-op">)</tt> </tt>
<a name="L1017"></a><tt class="py-lineno">1017</tt>  <tt class="py-line">                </tt>
<a name="L1018"></a><tt class="py-lineno">1018</tt>  <tt class="py-line">     </tt>
<a name="fol_bc_ask"></a><div id="fol_bc_ask-def"><a name="L1019"></a><tt class="py-lineno">1019</tt> <a class="py-toggle" href="#" id="fol_bc_ask-toggle" onclick="return toggle('fol_bc_ask');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#fol_bc_ask">fol_bc_ask</a><tt class="py-op">(</tt><tt class="py-param">KB</tt><tt class="py-op">,</tt> <tt class="py-param">goals</tt><tt class="py-op">,</tt> <tt class="py-param">theta</tt><tt class="py-op">=</tt><tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="fol_bc_ask-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="fol_bc_ask-expanded"><a name="L1020"></a><tt class="py-lineno">1020</tt>  <tt class="py-line">    <tt class="py-docstring">"""A simple backward-chaining algorithm for first-order logic. [Fig. 9.6]</tt> </tt>
<a name="L1021"></a><tt class="py-lineno">1021</tt>  <tt class="py-line"><tt class="py-docstring">    KB should be an instance of FolKB, and goals a list of literals.</tt> </tt>
<a name="L1022"></a><tt class="py-lineno">1022</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1023"></a><tt class="py-lineno">1023</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; test_ask('Farmer(x)')</tt> </tt>
<a name="L1024"></a><tt class="py-lineno">1024</tt>  <tt class="py-line"><tt class="py-docstring">    ['{x: Mac}']</tt> </tt>
<a name="L1025"></a><tt class="py-lineno">1025</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; test_ask('Human(x)')</tt> </tt>
<a name="L1026"></a><tt class="py-lineno">1026</tt>  <tt class="py-line"><tt class="py-docstring">    ['{x: Mac}', '{x: MrsMac}']</tt> </tt>
<a name="L1027"></a><tt class="py-lineno">1027</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; test_ask('Hates(x, y)')</tt> </tt>
<a name="L1028"></a><tt class="py-lineno">1028</tt>  <tt class="py-line"><tt class="py-docstring">    ['{x: Mac, y: Pete}']</tt> </tt>
<a name="L1029"></a><tt class="py-lineno">1029</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; test_ask('Loves(x, y)')</tt> </tt>
<a name="L1030"></a><tt class="py-lineno">1030</tt>  <tt class="py-line"><tt class="py-docstring">    ['{x: MrsMac, y: Mac}', '{x: MrsRabbit, y: Pete}']</tt> </tt>
<a name="L1031"></a><tt class="py-lineno">1031</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; test_ask('Rabbit(x)')</tt> </tt>
<a name="L1032"></a><tt class="py-lineno">1032</tt>  <tt class="py-line"><tt class="py-docstring">    ['{x: MrsRabbit}', '{x: Pete}']</tt> </tt>
<a name="L1033"></a><tt class="py-lineno">1033</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L1034"></a><tt class="py-lineno">1034</tt>  <tt class="py-line"> </tt>
<a name="L1035"></a><tt class="py-lineno">1035</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">goals</tt> <tt class="py-op">==</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">:</tt> </tt>
<a name="L1036"></a><tt class="py-lineno">1036</tt>  <tt class="py-line">        <tt class="py-keyword">yield</tt> <tt class="py-name">theta</tt> </tt>
<a name="L1037"></a><tt class="py-lineno">1037</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">StopIteration</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1038"></a><tt class="py-lineno">1038</tt>  <tt class="py-line">     </tt>
<a name="L1039"></a><tt class="py-lineno">1039</tt>  <tt class="py-line">    <tt class="py-name">q1</tt> <tt class="py-op">=</tt> <tt id="link-387" class="py-name"><a title="spade.logic.subst" class="py-name" href="#" onclick="return doclink('link-387', 'subst', 'link-335');">subst</a></tt><tt class="py-op">(</tt><tt class="py-name">theta</tt><tt class="py-op">,</tt> <tt class="py-name">goals</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L1040"></a><tt class="py-lineno">1040</tt>  <tt class="py-line"> </tt>
<a name="L1041"></a><tt class="py-lineno">1041</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-name">r</tt> <tt class="py-keyword">in</tt> <tt id="link-388" class="py-name"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-388', 'KB', 'link-169');">KB</a></tt><tt class="py-op">.</tt><tt class="py-name">clauses</tt><tt class="py-op">:</tt> </tt>
<a name="L1042"></a><tt class="py-lineno">1042</tt>  <tt class="py-line">        <tt class="py-name">sar</tt> <tt class="py-op">=</tt> <tt id="link-389" class="py-name"><a title="spade.logic.standardize_apart" class="py-name" href="#" onclick="return doclink('link-389', 'standardize_apart', 'link-353');">standardize_apart</a></tt><tt class="py-op">(</tt><tt class="py-name">r</tt><tt class="py-op">)</tt> </tt>
<a name="L1043"></a><tt class="py-lineno">1043</tt>  <tt class="py-line">         </tt>
<a name="L1044"></a><tt class="py-lineno">1044</tt>  <tt class="py-line">        <tt class="py-comment"># Split into head and body</tt> </tt>
<a name="L1045"></a><tt class="py-lineno">1045</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt id="link-390" class="py-name"><a title="spade.logic.is_symbol" class="py-name" href="#" onclick="return doclink('link-390', 'is_symbol', 'link-25');">is_symbol</a></tt><tt class="py-op">(</tt><tt class="py-name">sar</tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1046"></a><tt class="py-lineno">1046</tt>  <tt class="py-line">            <tt class="py-name">head</tt> <tt class="py-op">=</tt> <tt class="py-name">sar</tt> </tt>
<a name="L1047"></a><tt class="py-lineno">1047</tt>  <tt class="py-line">            <tt id="link-391" class="py-name" targets="Method spade.xmppd.modules.webadmin.WebAdminHandler.body()=spade.xmppd.modules.webadmin.WebAdminHandler-class.html#body"><a title="spade.xmppd.modules.webadmin.WebAdminHandler.body" class="py-name" href="#" onclick="return doclink('link-391', 'body', 'link-391');">body</a></tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt> </tt>
<a name="L1048"></a><tt class="py-lineno">1048</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">sar</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'&gt;&gt;'</tt><tt class="py-op">:</tt> <tt class="py-comment"># sar = (Body1 &amp; Body2 &amp; ...) &gt;&gt; Head</tt> </tt>
<a name="L1049"></a><tt class="py-lineno">1049</tt>  <tt class="py-line">            <tt class="py-name">head</tt> <tt class="py-op">=</tt> <tt class="py-name">sar</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L1050"></a><tt class="py-lineno">1050</tt>  <tt class="py-line">            <tt id="link-392" class="py-name"><a title="spade.xmppd.modules.webadmin.WebAdminHandler.body" class="py-name" href="#" onclick="return doclink('link-392', 'body', 'link-391');">body</a></tt> <tt class="py-op">=</tt> <tt class="py-name">sar</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-comment"># as conjunction</tt> </tt>
<a name="L1051"></a><tt class="py-lineno">1051</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L1052"></a><tt class="py-lineno">1052</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">Exception</tt><tt class="py-op">(</tt><tt class="py-string">"Invalid clause in FolKB: %s"</tt> <tt class="py-op">%</tt> <tt class="py-name">r</tt><tt class="py-op">)</tt> </tt>
<a name="L1053"></a><tt class="py-lineno">1053</tt>  <tt class="py-line"> </tt>
<a name="L1054"></a><tt class="py-lineno">1054</tt>  <tt class="py-line">        <tt class="py-name">theta1</tt> <tt class="py-op">=</tt> <tt id="link-393" class="py-name"><a title="spade.logic.unify" class="py-name" href="#" onclick="return doclink('link-393', 'unify', 'link-282');">unify</a></tt><tt class="py-op">(</tt><tt class="py-name">head</tt><tt class="py-op">,</tt> <tt class="py-name">q1</tt><tt class="py-op">,</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt><tt class="py-op">)</tt> </tt>
<a name="L1055"></a><tt class="py-lineno">1055</tt>  <tt class="py-line"> </tt>
<a name="L1056"></a><tt class="py-lineno">1056</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">theta1</tt> <tt class="py-keyword">is</tt> <tt class="py-keyword">not</tt> <tt class="py-name">None</tt><tt class="py-op">:</tt> </tt>
<a name="L1057"></a><tt class="py-lineno">1057</tt>  <tt class="py-line">            <tt class="py-keyword">if</tt> <tt id="link-394" class="py-name"><a title="spade.xmppd.modules.webadmin.WebAdminHandler.body" class="py-name" href="#" onclick="return doclink('link-394', 'body', 'link-391');">body</a></tt> <tt class="py-op">==</tt> <tt class="py-op">[</tt><tt class="py-op">]</tt><tt class="py-op">:</tt> </tt>
<a name="L1058"></a><tt class="py-lineno">1058</tt>  <tt class="py-line">                <tt class="py-name">new_goals</tt> <tt class="py-op">=</tt> <tt class="py-name">goals</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L1059"></a><tt class="py-lineno">1059</tt>  <tt class="py-line">            <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L1060"></a><tt class="py-lineno">1060</tt>  <tt class="py-line">                <tt class="py-name">new_goals</tt> <tt class="py-op">=</tt> <tt id="link-395" class="py-name"><a title="spade.logic.conjuncts" class="py-name" href="#" onclick="return doclink('link-395', 'conjuncts', 'link-13');">conjuncts</a></tt><tt class="py-op">(</tt><tt id="link-396" class="py-name"><a title="spade.xmppd.modules.webadmin.WebAdminHandler.body" class="py-name" href="#" onclick="return doclink('link-396', 'body', 'link-391');">body</a></tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">goals</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> </tt>
<a name="L1061"></a><tt class="py-lineno">1061</tt>  <tt class="py-line">             </tt>
<a name="L1062"></a><tt class="py-lineno">1062</tt>  <tt class="py-line">            <tt class="py-keyword">for</tt> <tt class="py-name">ans</tt> <tt class="py-keyword">in</tt> <tt id="link-397" class="py-name"><a title="spade.logic.fol_bc_ask" class="py-name" href="#" onclick="return doclink('link-397', 'fol_bc_ask', 'link-368');">fol_bc_ask</a></tt><tt class="py-op">(</tt><tt id="link-398" class="py-name"><a title="spade.logic.KB" class="py-name" href="#" onclick="return doclink('link-398', 'KB', 'link-169');">KB</a></tt><tt class="py-op">,</tt> <tt class="py-name">new_goals</tt><tt class="py-op">,</tt> <tt id="link-399" class="py-name" targets="Function spade.logic.subst_compose()=spade.logic-module.html#subst_compose"><a title="spade.logic.subst_compose" class="py-name" href="#" onclick="return doclink('link-399', 'subst_compose', 'link-399');">subst_compose</a></tt><tt class="py-op">(</tt><tt class="py-name">theta1</tt><tt class="py-op">,</tt> <tt class="py-name">theta</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1063"></a><tt class="py-lineno">1063</tt>  <tt class="py-line">                <tt class="py-keyword">yield</tt> <tt class="py-name">ans</tt> </tt>
<a name="L1064"></a><tt class="py-lineno">1064</tt>  <tt class="py-line"> </tt>
<a name="L1065"></a><tt class="py-lineno">1065</tt>  <tt class="py-line">    <tt class="py-keyword">raise</tt> <tt class="py-name">StopIteration</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1066"></a><tt class="py-lineno">1066</tt>  <tt class="py-line"> </tt>
<a name="subst_compose"></a><div id="subst_compose-def"><a name="L1067"></a><tt class="py-lineno">1067</tt> <a class="py-toggle" href="#" id="subst_compose-toggle" onclick="return toggle('subst_compose');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#subst_compose">subst_compose</a> <tt class="py-op">(</tt><tt class="py-param">s1</tt><tt class="py-op">,</tt> <tt class="py-param">s2</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="subst_compose-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="subst_compose-expanded"><a name="L1068"></a><tt class="py-lineno">1068</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return the substitution which is equivalent to applying s2 to</tt> </tt>
<a name="L1069"></a><tt class="py-lineno">1069</tt>  <tt class="py-line"><tt class="py-docstring">    the result of applying s1 to an expression.</tt> </tt>
<a name="L1070"></a><tt class="py-lineno">1070</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1071"></a><tt class="py-lineno">1071</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; s1 = {x: A, y: B}</tt> </tt>
<a name="L1072"></a><tt class="py-lineno">1072</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; s2 = {z: x, x: C}</tt> </tt>
<a name="L1073"></a><tt class="py-lineno">1073</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; p = F(x) &amp; G(y) &amp; expr('H(z)')</tt> </tt>
<a name="L1074"></a><tt class="py-lineno">1074</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(s1, p)</tt> </tt>
<a name="L1075"></a><tt class="py-lineno">1075</tt>  <tt class="py-line"><tt class="py-docstring">    ((F(A) &amp; G(B)) &amp; H(z))</tt> </tt>
<a name="L1076"></a><tt class="py-lineno">1076</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(s2, p)</tt> </tt>
<a name="L1077"></a><tt class="py-lineno">1077</tt>  <tt class="py-line"><tt class="py-docstring">    ((F(C) &amp; G(y)) &amp; H(x))</tt> </tt>
<a name="L1078"></a><tt class="py-lineno">1078</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L1079"></a><tt class="py-lineno">1079</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(s2, subst(s1, p))</tt> </tt>
<a name="L1080"></a><tt class="py-lineno">1080</tt>  <tt class="py-line"><tt class="py-docstring">    ((F(A) &amp; G(B)) &amp; H(x))</tt> </tt>
<a name="L1081"></a><tt class="py-lineno">1081</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(subst_compose(s1, s2), p)</tt> </tt>
<a name="L1082"></a><tt class="py-lineno">1082</tt>  <tt class="py-line"><tt class="py-docstring">    ((F(A) &amp; G(B)) &amp; H(x))</tt> </tt>
<a name="L1083"></a><tt class="py-lineno">1083</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1084"></a><tt class="py-lineno">1084</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(s1, subst(s2, p))</tt> </tt>
<a name="L1085"></a><tt class="py-lineno">1085</tt>  <tt class="py-line"><tt class="py-docstring">    ((F(C) &amp; G(B)) &amp; H(A))</tt> </tt>
<a name="L1086"></a><tt class="py-lineno">1086</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(subst_compose(s2, s1), p)</tt> </tt>
<a name="L1087"></a><tt class="py-lineno">1087</tt>  <tt class="py-line"><tt class="py-docstring">    ((F(C) &amp; G(B)) &amp; H(A))</tt> </tt>
<a name="L1088"></a><tt class="py-lineno">1088</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppsubst(subst_compose(s1, s2))</tt> </tt>
<a name="L1089"></a><tt class="py-lineno">1089</tt>  <tt class="py-line"><tt class="py-docstring">    {x: A, y: B, z: x}</tt> </tt>
<a name="L1090"></a><tt class="py-lineno">1090</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ppsubst(subst_compose(s2, s1))</tt> </tt>
<a name="L1091"></a><tt class="py-lineno">1091</tt>  <tt class="py-line"><tt class="py-docstring">    {x: C, y: B, z: A}</tt> </tt>
<a name="L1092"></a><tt class="py-lineno">1092</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(subst_compose(s1, s2), p) == subst(s2, subst(s1, p))</tt> </tt>
<a name="L1093"></a><tt class="py-lineno">1093</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L1094"></a><tt class="py-lineno">1094</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; subst(subst_compose(s2, s1), p) == subst(s1, subst(s2, p))</tt> </tt>
<a name="L1095"></a><tt class="py-lineno">1095</tt>  <tt class="py-line"><tt class="py-docstring">    True</tt> </tt>
<a name="L1096"></a><tt class="py-lineno">1096</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L1097"></a><tt class="py-lineno">1097</tt>  <tt class="py-line">    <tt class="py-name">sc</tt> <tt class="py-op">=</tt> <tt class="py-op">{</tt><tt class="py-op">}</tt> </tt>
<a name="L1098"></a><tt class="py-lineno">1098</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt id="link-400" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-400', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">v</tt> <tt class="py-keyword">in</tt> <tt class="py-name">s1</tt><tt class="py-op">.</tt><tt id="link-401" class="py-name"><a title="spade.pyparsing.ParseResults.items" class="py-name" href="#" onclick="return doclink('link-401', 'items', 'link-382');">items</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1099"></a><tt class="py-lineno">1099</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">s2</tt><tt class="py-op">.</tt><tt class="py-name">has_key</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1100"></a><tt class="py-lineno">1100</tt>  <tt class="py-line">            <tt class="py-name">w</tt> <tt class="py-op">=</tt> <tt class="py-name">s2</tt><tt class="py-op">[</tt><tt class="py-name">v</tt><tt class="py-op">]</tt> </tt>
<a name="L1101"></a><tt class="py-lineno">1101</tt>  <tt class="py-line">            <tt class="py-name">sc</tt><tt class="py-op">[</tt><tt id="link-402" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-402', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">w</tt> <tt class="py-comment"># x -&gt; v -&gt; w</tt> </tt>
<a name="L1102"></a><tt class="py-lineno">1102</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L1103"></a><tt class="py-lineno">1103</tt>  <tt class="py-line">            <tt class="py-name">sc</tt><tt class="py-op">[</tt><tt id="link-403" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-403', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">v</tt> </tt>
<a name="L1104"></a><tt class="py-lineno">1104</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt id="link-404" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-404', 'x', 'link-0');">x</a></tt><tt class="py-op">,</tt> <tt class="py-name">v</tt> <tt class="py-keyword">in</tt> <tt class="py-name">s2</tt><tt class="py-op">.</tt><tt id="link-405" class="py-name"><a title="spade.pyparsing.ParseResults.items" class="py-name" href="#" onclick="return doclink('link-405', 'items', 'link-382');">items</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1105"></a><tt class="py-lineno">1105</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-op">(</tt><tt class="py-name">s1</tt><tt class="py-op">.</tt><tt class="py-name">has_key</tt><tt class="py-op">(</tt><tt id="link-406" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-406', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1106"></a><tt class="py-lineno">1106</tt>  <tt class="py-line">            <tt class="py-name">sc</tt><tt class="py-op">[</tt><tt id="link-407" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-407', 'x', 'link-0');">x</a></tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">v</tt> </tt>
<a name="L1107"></a><tt class="py-lineno">1107</tt>  <tt class="py-line">        <tt class="py-comment"># otherwise s1[x] preemptys s2[x]</tt> </tt>
<a name="L1108"></a><tt class="py-lineno">1108</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">sc</tt> </tt>
</div><a name="L1109"></a><tt class="py-lineno">1109</tt>  <tt class="py-line"> </tt>
<a name="L1110"></a><tt class="py-lineno">1110</tt>  <tt class="py-line"><tt class="py-comment">#______________________________________________________________________________</tt> </tt>
<a name="L1111"></a><tt class="py-lineno">1111</tt>  <tt class="py-line"> </tt>
<a name="L1112"></a><tt class="py-lineno">1112</tt>  <tt class="py-line"><tt class="py-comment"># Example application (not in the book).</tt> </tt>
<a name="L1113"></a><tt class="py-lineno">1113</tt>  <tt class="py-line"><tt class="py-comment"># You can use the Expr class to do symbolic differentiation.  This used to be</tt> </tt>
<a name="L1114"></a><tt class="py-lineno">1114</tt>  <tt class="py-line"><tt class="py-comment"># a part of AI; now it is considered a separate field, Symbolic Algebra.</tt> </tt>
<a name="L1115"></a><tt class="py-lineno">1115</tt>  <tt class="py-line"> </tt>
<a name="diff"></a><div id="diff-def"><a name="L1116"></a><tt class="py-lineno">1116</tt> <a class="py-toggle" href="#" id="diff-toggle" onclick="return toggle('diff');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#diff">diff</a><tt class="py-op">(</tt><tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="diff-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="diff-expanded"><a name="L1117"></a><tt class="py-lineno">1117</tt>  <tt class="py-line">    <tt class="py-docstring">"""Return the symbolic derivative, dy/dx, as an Expr.</tt> </tt>
<a name="L1118"></a><tt class="py-lineno">1118</tt>  <tt class="py-line"><tt class="py-docstring">    However, you probably want to simplify the results with simp.</tt> </tt>
<a name="L1119"></a><tt class="py-lineno">1119</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; diff(x * x, x)</tt> </tt>
<a name="L1120"></a><tt class="py-lineno">1120</tt>  <tt class="py-line"><tt class="py-docstring">    ((x * 1) + (x * 1))</tt> </tt>
<a name="L1121"></a><tt class="py-lineno">1121</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; simp(diff(x * x, x))</tt> </tt>
<a name="L1122"></a><tt class="py-lineno">1122</tt>  <tt class="py-line"><tt class="py-docstring">    (2 * x)</tt> </tt>
<a name="L1123"></a><tt class="py-lineno">1123</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L1124"></a><tt class="py-lineno">1124</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-408" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-408', 'y', 'link-81');">y</a></tt> <tt class="py-op">==</tt> <tt id="link-409" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-409', 'x', 'link-0');">x</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-410" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-410', 'ONE', 'link-70');">ONE</a></tt> </tt>
<a name="L1125"></a><tt class="py-lineno">1125</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-keyword">not</tt> <tt id="link-411" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-411', 'y', 'link-81');">y</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-412" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-412', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1126"></a><tt class="py-lineno">1126</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L1127"></a><tt class="py-lineno">1127</tt>  <tt class="py-line">        <tt class="py-name">u</tt><tt class="py-op">,</tt> <tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt id="link-413" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-413', 'y', 'link-81');">y</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt id="link-414" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-414', 'y', 'link-81');">y</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt id="link-415" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-415', 'y', 'link-81');">y</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L1128"></a><tt class="py-lineno">1128</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'+'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-416" class="py-name" targets="Function spade.logic.diff()=spade.logic-module.html#diff"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-416', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-417" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-417', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt id="link-418" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-418', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt> <tt id="link-419" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-419', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1129"></a><tt class="py-lineno">1129</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'-'</tt> <tt class="py-keyword">and</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt id="link-420" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-420', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-421" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-421', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1130"></a><tt class="py-lineno">1130</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'-'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-422" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-422', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-423" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-423', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt id="link-424" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-424', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt> <tt id="link-425" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-425', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1131"></a><tt class="py-lineno">1131</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'*'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt> <tt class="py-op">*</tt> <tt id="link-426" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-426', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt> <tt id="link-427" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-427', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">v</tt> <tt class="py-op">*</tt> <tt id="link-428" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-428', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-429" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-429', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1132"></a><tt class="py-lineno">1132</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'/'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">*</tt><tt id="link-430" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-430', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-431" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-431', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">u</tt><tt class="py-op">*</tt><tt id="link-432" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-432', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt> <tt id="link-433" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-433', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">/</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt> <tt class="py-op">*</tt> <tt class="py-name">v</tt><tt class="py-op">)</tt> </tt>
<a name="L1133"></a><tt class="py-lineno">1133</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'**'</tt> <tt class="py-keyword">and</tt> <tt id="link-434" class="py-name"><a title="spade.logic.isnumber" class="py-name" href="#" onclick="return doclink('link-434', 'isnumber', 'link-4');">isnumber</a></tt><tt class="py-op">(</tt><tt id="link-435" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-435', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1134"></a><tt class="py-lineno">1134</tt>  <tt class="py-line">            <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt> <tt class="py-op">*</tt> <tt class="py-name">u</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt id="link-436" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-436', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-437" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-437', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L1135"></a><tt class="py-lineno">1135</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'**'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt> <tt class="py-op">*</tt> <tt class="py-name">u</tt> <tt class="py-op">**</tt> <tt class="py-op">(</tt><tt class="py-name">v</tt> <tt class="py-op">-</tt> <tt class="py-number">1</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt id="link-438" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-438', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-439" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-439', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1136"></a><tt class="py-lineno">1136</tt>  <tt class="py-line">                                 <tt class="py-op">+</tt> <tt class="py-name">u</tt> <tt class="py-op">**</tt> <tt class="py-name">v</tt> <tt class="py-op">*</tt> <tt id="link-440" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-440', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'log'</tt><tt class="py-op">)</tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt id="link-441" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-441', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">,</tt> <tt id="link-442" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-442', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L1137"></a><tt class="py-lineno">1137</tt>  <tt class="py-line">        <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'log'</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-443" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-443', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">,</tt> <tt id="link-444" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-444', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> <tt class="py-op">/</tt> <tt class="py-name">u</tt> </tt>
<a name="L1138"></a><tt class="py-lineno">1138</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">"Unknown op: %s in diff(%s, %s)"</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt id="link-445" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-445', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt id="link-446" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-446', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1139"></a><tt class="py-lineno">1139</tt>  <tt class="py-line"> </tt>
<a name="simp"></a><div id="simp-def"><a name="L1140"></a><tt class="py-lineno">1140</tt> <a class="py-toggle" href="#" id="simp-toggle" onclick="return toggle('simp');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#simp">simp</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="simp-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="simp-expanded"><a name="L1141"></a><tt class="py-lineno">1141</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt id="link-447" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-447', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-448" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-448', 'x', 'link-0');">x</a></tt> </tt>
<a name="L1142"></a><tt class="py-lineno">1142</tt>  <tt class="py-line">    <tt class="py-name">args</tt> <tt class="py-op">=</tt> <tt class="py-name">map</tt><tt class="py-op">(</tt><tt id="link-449" class="py-name" targets="Function spade.logic.simp()=spade.logic-module.html#simp"><a title="spade.logic.simp" class="py-name" href="#" onclick="return doclink('link-449', 'simp', 'link-449');">simp</a></tt><tt class="py-op">,</tt> <tt id="link-450" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-450', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
<a name="L1143"></a><tt class="py-lineno">1143</tt>  <tt class="py-line">    <tt class="py-name">u</tt><tt class="py-op">,</tt> <tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt id="link-451" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-451', 'x', 'link-0');">x</a></tt><tt class="py-op">.</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L1144"></a><tt class="py-lineno">1144</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'+'</tt><tt class="py-op">:</tt>  </tt>
<a name="L1145"></a><tt class="py-lineno">1145</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-452" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-452', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt> </tt>
<a name="L1146"></a><tt class="py-lineno">1146</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-453" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-453', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">v</tt> </tt>
<a name="L1147"></a><tt class="py-lineno">1147</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-name">v</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-454" class="py-name"><a title="spade.bdi.TWO
spade.logic.TWO" class="py-name" href="#" onclick="return doclink('link-454', 'TWO', 'link-71');">TWO</a></tt> <tt class="py-op">*</tt> <tt class="py-name">u</tt> </tt>
<a name="L1148"></a><tt class="py-lineno">1148</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-op">-</tt><tt class="py-name">v</tt> <tt class="py-keyword">or</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt class="py-op">-</tt><tt class="py-name">u</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-455" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-455', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1149"></a><tt class="py-lineno">1149</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'-'</tt> <tt class="py-keyword">and</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt>  </tt>
<a name="L1150"></a><tt class="py-lineno">1150</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt><tt class="py-op">.</tt><tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'-'</tt> <tt class="py-keyword">and</tt> <tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">u</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> <tt class="py-op">==</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt><tt class="py-op">.</tt><tt class="py-name">args</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-comment">## --y ==&gt; y</tt> </tt>
<a name="L1151"></a><tt class="py-lineno">1151</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'-'</tt><tt class="py-op">:</tt>  </tt>
<a name="L1152"></a><tt class="py-lineno">1152</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-456" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-456', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt> </tt>
<a name="L1153"></a><tt class="py-lineno">1153</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-457" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-457', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-op">-</tt><tt class="py-name">v</tt> </tt>
<a name="L1154"></a><tt class="py-lineno">1154</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-name">v</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-458" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-458', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1155"></a><tt class="py-lineno">1155</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-op">-</tt><tt class="py-name">v</tt> <tt class="py-keyword">or</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt class="py-op">-</tt><tt class="py-name">u</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-459" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-459', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1156"></a><tt class="py-lineno">1156</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'*'</tt><tt class="py-op">:</tt>  </tt>
<a name="L1157"></a><tt class="py-lineno">1157</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-460" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-460', 'ZERO', 'link-69');">ZERO</a></tt> <tt class="py-keyword">or</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-461" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-461', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-462" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-462', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1158"></a><tt class="py-lineno">1158</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-463" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-463', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">v</tt> </tt>
<a name="L1159"></a><tt class="py-lineno">1159</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-464" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-464', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt> </tt>
<a name="L1160"></a><tt class="py-lineno">1160</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-name">v</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt> <tt class="py-op">**</tt> <tt class="py-number">2</tt> </tt>
<a name="L1161"></a><tt class="py-lineno">1161</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'/'</tt><tt class="py-op">:</tt>  </tt>
<a name="L1162"></a><tt class="py-lineno">1162</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-465" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-465', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-466" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-466', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1163"></a><tt class="py-lineno">1163</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-467" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-467', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-468" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-468', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-string">'Undefined'</tt><tt class="py-op">)</tt> </tt>
<a name="L1164"></a><tt class="py-lineno">1164</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-name">v</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-469" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-469', 'ONE', 'link-70');">ONE</a></tt> </tt>
<a name="L1165"></a><tt class="py-lineno">1165</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt class="py-op">-</tt><tt class="py-name">v</tt> <tt class="py-keyword">or</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt class="py-op">-</tt><tt class="py-name">u</tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-470" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-470', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1166"></a><tt class="py-lineno">1166</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'**'</tt><tt class="py-op">:</tt>  </tt>
<a name="L1167"></a><tt class="py-lineno">1167</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-471" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-471', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-472" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-472', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1168"></a><tt class="py-lineno">1168</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-473" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-473', 'ZERO', 'link-69');">ZERO</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-474" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-474', 'ONE', 'link-70');">ONE</a></tt> </tt>
<a name="L1169"></a><tt class="py-lineno">1169</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-475" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-475', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-476" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-476', 'ONE', 'link-70');">ONE</a></tt> </tt>
<a name="L1170"></a><tt class="py-lineno">1170</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">v</tt> <tt class="py-op">==</tt> <tt id="link-477" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-477', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt class="py-name">u</tt> </tt>
<a name="L1171"></a><tt class="py-lineno">1171</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">op</tt> <tt class="py-op">==</tt> <tt class="py-string">'log'</tt><tt class="py-op">:</tt>  </tt>
<a name="L1172"></a><tt class="py-lineno">1172</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">u</tt> <tt class="py-op">==</tt> <tt id="link-478" class="py-name"><a title="spade.bdi.ONE
spade.logic.ONE" class="py-name" href="#" onclick="return doclink('link-478', 'ONE', 'link-70');">ONE</a></tt><tt class="py-op">:</tt> <tt class="py-keyword">return</tt> <tt id="link-479" class="py-name"><a title="spade.bdi.ZERO
spade.logic.ZERO" class="py-name" href="#" onclick="return doclink('link-479', 'ZERO', 'link-69');">ZERO</a></tt> </tt>
<a name="L1173"></a><tt class="py-lineno">1173</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">"Unknown op: "</tt> <tt class="py-op">+</tt> <tt class="py-name">op</tt><tt class="py-op">)</tt> </tt>
<a name="L1174"></a><tt class="py-lineno">1174</tt>  <tt class="py-line">    <tt class="py-comment">## If we fall through to here, we can not simplify further</tt> </tt>
<a name="L1175"></a><tt class="py-lineno">1175</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-480" class="py-name"><a title="spade.logic.Expr" class="py-name" href="#" onclick="return doclink('link-480', 'Expr', 'link-16');">Expr</a></tt><tt class="py-op">(</tt><tt class="py-name">op</tt><tt class="py-op">,</tt> <tt class="py-op">*</tt><tt class="py-name">args</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1176"></a><tt class="py-lineno">1176</tt>  <tt class="py-line"> </tt>
<a name="d"></a><div id="d-def"><a name="L1177"></a><tt class="py-lineno">1177</tt> <a class="py-toggle" href="#" id="d-toggle" onclick="return toggle('d');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#d">d</a><tt class="py-op">(</tt><tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="d-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="d-expanded"><a name="L1178"></a><tt class="py-lineno">1178</tt>  <tt class="py-line">    <tt class="py-docstring">"Differentiate and then simplify."</tt> </tt>
<a name="L1179"></a><tt class="py-lineno">1179</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt id="link-481" class="py-name"><a title="spade.logic.simp" class="py-name" href="#" onclick="return doclink('link-481', 'simp', 'link-449');">simp</a></tt><tt class="py-op">(</tt><tt id="link-482" class="py-name"><a title="spade.logic.diff" class="py-name" href="#" onclick="return doclink('link-482', 'diff', 'link-416');">diff</a></tt><tt class="py-op">(</tt><tt id="link-483" class="py-name"><a title="spade.bdi.y
spade.logic.y" class="py-name" href="#" onclick="return doclink('link-483', 'y', 'link-81');">y</a></tt><tt class="py-op">,</tt> <tt id="link-484" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-484', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt><tt class="py-op">)</tt>     </tt>
</div><a name="L1180"></a><tt class="py-lineno">1180</tt>  <tt class="py-line"> </tt>
<a name="L1181"></a><tt class="py-lineno">1181</tt>  <tt class="py-line"><tt class="py-comment">#_______________________________________________________________________________</tt> </tt>
<a name="L1182"></a><tt class="py-lineno">1182</tt>  <tt class="py-line"> </tt>
<a name="L1183"></a><tt class="py-lineno">1183</tt>  <tt class="py-line"><tt class="py-comment"># Utilities for doctest cases</tt> </tt>
<a name="L1184"></a><tt class="py-lineno">1184</tt>  <tt class="py-line"><tt class="py-comment"># These functions print their arguments in a standard order</tt> </tt>
<a name="L1185"></a><tt class="py-lineno">1185</tt>  <tt class="py-line"><tt class="py-comment"># to compensate for the random order in the standard representation</tt> </tt>
<a name="L1186"></a><tt class="py-lineno">1186</tt>  <tt class="py-line"> </tt>
<a name="pretty"></a><div id="pretty-def"><a name="L1187"></a><tt class="py-lineno">1187</tt> <a class="py-toggle" href="#" id="pretty-toggle" onclick="return toggle('pretty');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pretty">pretty</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pretty-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pretty-expanded"><a name="L1188"></a><tt class="py-lineno">1188</tt>  <tt class="py-line">    <tt class="py-name">t</tt> <tt class="py-op">=</tt> <tt class="py-name">type</tt><tt class="py-op">(</tt><tt id="link-485" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-485', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1189"></a><tt class="py-lineno">1189</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">t</tt> <tt class="py-op">==</tt> <tt class="py-name">dict</tt><tt class="py-op">:</tt> </tt>
<a name="L1190"></a><tt class="py-lineno">1190</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-486" class="py-name" targets="Function spade.logic.pretty_dict()=spade.logic-module.html#pretty_dict"><a title="spade.logic.pretty_dict" class="py-name" href="#" onclick="return doclink('link-486', 'pretty_dict', 'link-486');">pretty_dict</a></tt><tt class="py-op">(</tt><tt id="link-487" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-487', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
<a name="L1191"></a><tt class="py-lineno">1191</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">t</tt> <tt class="py-op">==</tt> <tt class="py-name">set</tt><tt class="py-op">:</tt> </tt>
<a name="L1192"></a><tt class="py-lineno">1192</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-488" class="py-name" targets="Function spade.logic.pretty_set()=spade.logic-module.html#pretty_set"><a title="spade.logic.pretty_set" class="py-name" href="#" onclick="return doclink('link-488', 'pretty_set', 'link-488');">pretty_set</a></tt><tt class="py-op">(</tt><tt id="link-489" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-489', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L1193"></a><tt class="py-lineno">1193</tt>  <tt class="py-line"> </tt>
<a name="pretty_dict"></a><div id="pretty_dict-def"><a name="L1194"></a><tt class="py-lineno">1194</tt> <a class="py-toggle" href="#" id="pretty_dict-toggle" onclick="return toggle('pretty_dict');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pretty_dict">pretty_dict</a><tt class="py-op">(</tt><tt class="py-param">d</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pretty_dict-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pretty_dict-expanded"><a name="L1195"></a><tt class="py-lineno">1195</tt>  <tt class="py-line">    <tt class="py-docstring">"""Print the dictionary d.</tt> </tt>
<a name="L1196"></a><tt class="py-lineno">1196</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L1197"></a><tt class="py-lineno">1197</tt>  <tt class="py-line"><tt class="py-docstring">    Prints a string representation of the dictionary</tt> </tt>
<a name="L1198"></a><tt class="py-lineno">1198</tt>  <tt class="py-line"><tt class="py-docstring">    with keys in sorted order according to their string</tt> </tt>
<a name="L1199"></a><tt class="py-lineno">1199</tt>  <tt class="py-line"><tt class="py-docstring">    representation: {a: A, d: D, ...}.</tt> </tt>
<a name="L1200"></a><tt class="py-lineno">1200</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; pretty_dict({'m': 'M', 'a': 'A', 'r': 'R', 'k': 'K'})</tt> </tt>
<a name="L1201"></a><tt class="py-lineno">1201</tt>  <tt class="py-line"><tt class="py-docstring">    "{'a': 'A', 'k': 'K', 'm': 'M', 'r': 'R'}"</tt> </tt>
<a name="L1202"></a><tt class="py-lineno">1202</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; pretty_dict({z: C, y: B, x: A})</tt> </tt>
<a name="L1203"></a><tt class="py-lineno">1203</tt>  <tt class="py-line"><tt class="py-docstring">    '{x: A, y: B, z: C}'</tt> </tt>
<a name="L1204"></a><tt class="py-lineno">1204</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L1205"></a><tt class="py-lineno">1205</tt>  <tt class="py-line"> </tt>
<a name="L1206"></a><tt class="py-lineno">1206</tt>  <tt class="py-line">    <tt class="py-keyword">def</tt> <tt class="py-def-name">format</tt><tt class="py-op">(</tt><tt class="py-param">k</tt><tt class="py-op">,</tt> <tt class="py-param">v</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L1207"></a><tt class="py-lineno">1207</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-string">"%s: %s"</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">repr</tt><tt class="py-op">(</tt><tt class="py-name">k</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">repr</tt><tt class="py-op">(</tt><tt class="py-name">v</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1208"></a><tt class="py-lineno">1208</tt>  <tt class="py-line"> </tt>
<a name="L1209"></a><tt class="py-lineno">1209</tt>  <tt class="py-line">    <tt class="py-name">ditems</tt> <tt class="py-op">=</tt> <tt id="link-490" class="py-name"><a title="spade.logic.d" class="py-name" href="#" onclick="return doclink('link-490', 'd', 'link-145');">d</a></tt><tt class="py-op">.</tt><tt id="link-491" class="py-name"><a title="spade.pyparsing.ParseResults.items" class="py-name" href="#" onclick="return doclink('link-491', 'items', 'link-382');">items</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L1210"></a><tt class="py-lineno">1210</tt>  <tt class="py-line">    <tt class="py-name">ditems</tt><tt class="py-op">.</tt><tt class="py-name">sort</tt><tt class="py-op">(</tt><tt class="py-name">key</tt><tt class="py-op">=</tt><tt class="py-name">str</tt><tt class="py-op">)</tt> </tt>
<a name="L1211"></a><tt class="py-lineno">1211</tt>  <tt class="py-line">    <tt class="py-name">k</tt><tt class="py-op">,</tt> <tt class="py-name">v</tt> <tt class="py-op">=</tt> <tt class="py-name">ditems</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L1212"></a><tt class="py-lineno">1212</tt>  <tt class="py-line">    <tt class="py-name">dpairs</tt> <tt class="py-op">=</tt> <tt class="py-name">format</tt><tt class="py-op">(</tt><tt class="py-name">k</tt><tt class="py-op">,</tt> <tt class="py-name">v</tt><tt class="py-op">)</tt> </tt>
<a name="L1213"></a><tt class="py-lineno">1213</tt>  <tt class="py-line">    <tt class="py-keyword">for</tt> <tt class="py-op">(</tt><tt class="py-name">k</tt><tt class="py-op">,</tt> <tt class="py-name">v</tt><tt class="py-op">)</tt> <tt class="py-keyword">in</tt> <tt class="py-name">ditems</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">:</tt> </tt>
<a name="L1214"></a><tt class="py-lineno">1214</tt>  <tt class="py-line">        <tt class="py-name">dpairs</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-string">', '</tt> <tt class="py-op">+</tt> <tt class="py-name">format</tt><tt class="py-op">(</tt><tt class="py-name">k</tt><tt class="py-op">,</tt> <tt class="py-name">v</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L1215"></a><tt class="py-lineno">1215</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-string">'{%s}'</tt> <tt class="py-op">%</tt> <tt class="py-name">dpairs</tt> </tt>
</div><a name="L1216"></a><tt class="py-lineno">1216</tt>  <tt class="py-line"> </tt>
<a name="pretty_set"></a><div id="pretty_set-def"><a name="L1217"></a><tt class="py-lineno">1217</tt> <a class="py-toggle" href="#" id="pretty_set-toggle" onclick="return toggle('pretty_set');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pretty_set">pretty_set</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pretty_set-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pretty_set-expanded"><a name="L1218"></a><tt class="py-lineno">1218</tt>  <tt class="py-line">    <tt class="py-docstring">"""Print the set s.</tt> </tt>
<a name="L1219"></a><tt class="py-lineno">1219</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L1220"></a><tt class="py-lineno">1220</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; pretty_set(set(['A', 'Q', 'F', 'K', 'Y', 'B']))</tt> </tt>
<a name="L1221"></a><tt class="py-lineno">1221</tt>  <tt class="py-line"><tt class="py-docstring">    "set(['A', 'B', 'F', 'K', 'Q', 'Y'])"</tt> </tt>
<a name="L1222"></a><tt class="py-lineno">1222</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; pretty_set(set([z, y, x]))</tt> </tt>
<a name="L1223"></a><tt class="py-lineno">1223</tt>  <tt class="py-line"><tt class="py-docstring">    'set([x, y, z])'</tt> </tt>
<a name="L1224"></a><tt class="py-lineno">1224</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L1225"></a><tt class="py-lineno">1225</tt>  <tt class="py-line"> </tt>
<a name="L1226"></a><tt class="py-lineno">1226</tt>  <tt class="py-line">    <tt class="py-name">slist</tt> <tt class="py-op">=</tt> <tt class="py-name">list</tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
<a name="L1227"></a><tt class="py-lineno">1227</tt>  <tt class="py-line">    <tt class="py-name">slist</tt><tt class="py-op">.</tt><tt class="py-name">sort</tt><tt class="py-op">(</tt><tt class="py-name">key</tt><tt class="py-op">=</tt><tt class="py-name">str</tt><tt class="py-op">)</tt> </tt>
<a name="L1228"></a><tt class="py-lineno">1228</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-string">'set(%s)'</tt> <tt class="py-op">%</tt> <tt class="py-name">slist</tt> </tt>
</div><a name="L1229"></a><tt class="py-lineno">1229</tt>  <tt class="py-line"> </tt>
<a name="pp"></a><div id="pp-def"><a name="L1230"></a><tt class="py-lineno">1230</tt> <a class="py-toggle" href="#" id="pp-toggle" onclick="return toggle('pp');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#pp">pp</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="pp-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="pp-expanded"><a name="L1231"></a><tt class="py-lineno">1231</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt id="link-492" class="py-name"><a title="spade.logic.pretty" class="py-name" href="#" onclick="return doclink('link-492', 'pretty', 'link-378');">pretty</a></tt><tt class="py-op">(</tt><tt id="link-493" class="py-name"><a title="spade.bdi.x
spade.logic.x" class="py-name" href="#" onclick="return doclink('link-493', 'x', 'link-0');">x</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L1232"></a><tt class="py-lineno">1232</tt>  <tt class="py-line">     </tt>
<a name="ppsubst"></a><div id="ppsubst-def"><a name="L1233"></a><tt class="py-lineno">1233</tt> <a class="py-toggle" href="#" id="ppsubst-toggle" onclick="return toggle('ppsubst');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#ppsubst">ppsubst</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ppsubst-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="ppsubst-expanded"><a name="L1234"></a><tt class="py-lineno">1234</tt>  <tt class="py-line">    <tt class="py-docstring">"""Pretty-print substitution s"""</tt> </tt>
<a name="L1235"></a><tt class="py-lineno">1235</tt>  <tt class="py-line">    <tt id="link-494" class="py-name" targets="Function spade.logic.ppdict()=spade.logic-module.html#ppdict"><a title="spade.logic.ppdict" class="py-name" href="#" onclick="return doclink('link-494', 'ppdict', 'link-494');">ppdict</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1236"></a><tt class="py-lineno">1236</tt>  <tt class="py-line"> </tt>
<a name="ppdict"></a><div id="ppdict-def"><a name="L1237"></a><tt class="py-lineno">1237</tt> <a class="py-toggle" href="#" id="ppdict-toggle" onclick="return toggle('ppdict');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#ppdict">ppdict</a><tt class="py-op">(</tt><tt class="py-param">d</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ppdict-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="ppdict-expanded"><a name="L1238"></a><tt class="py-lineno">1238</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt id="link-495" class="py-name"><a title="spade.logic.pretty_dict" class="py-name" href="#" onclick="return doclink('link-495', 'pretty_dict', 'link-486');">pretty_dict</a></tt><tt class="py-op">(</tt><tt id="link-496" class="py-name"><a title="spade.logic.d" class="py-name" href="#" onclick="return doclink('link-496', 'd', 'link-145');">d</a></tt><tt class="py-op">)</tt> </tt>
</div><a name="L1239"></a><tt class="py-lineno">1239</tt>  <tt class="py-line"> </tt>
<a name="ppset"></a><div id="ppset-def"><a name="L1240"></a><tt class="py-lineno">1240</tt> <a class="py-toggle" href="#" id="ppset-toggle" onclick="return toggle('ppset');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="spade.logic-module.html#ppset">ppset</a><tt class="py-op">(</tt><tt class="py-param">s</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="ppset-collapsed" style="display:none;" pad="++++" indent="++++"></div><div id="ppset-expanded"><a name="L1241"></a><tt class="py-lineno">1241</tt>  <tt class="py-line">    <tt class="py-keyword">print</tt> <tt id="link-497" class="py-name"><a title="spade.logic.pretty_set" class="py-name" href="#" onclick="return doclink('link-497', 'pretty_set', 'link-488');">pretty_set</a></tt><tt class="py-op">(</tt><tt class="py-name">s</tt><tt class="py-op">)</tt> </tt>
</div><a name="L1242"></a><tt class="py-lineno">1242</tt>  <tt class="py-line"> </tt>
<a name="L1243"></a><tt class="py-lineno">1243</tt>  <tt class="py-line"><tt class="py-comment">#________________________________________________________________________</tt> </tt>
<a name="L1244"></a><tt class="py-lineno">1244</tt>  <tt class="py-line"> </tt>
<a name="logicTest"></a><div id="logicTest-def"><a name="L1245"></a><tt class="py-lineno">1245</tt> <a class="py-toggle" href="#" id="logicTest-toggle" onclick="return toggle('logicTest');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="spade.logic.logicTest-class.html">logicTest</a><tt class="py-op">:</tt> <tt class="py-string">"""</tt> </tt>
<a name="L1246"></a><tt class="py-lineno">1246</tt>  <tt class="py-line"><tt class="py-string">### PropKB</tt> </tt>
<a name="L1247"></a><tt class="py-lineno">1247</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb = PropKB()</tt> </tt>
<a name="L1248"></a><tt class="py-lineno">1248</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb.tell(A &amp; B)</tt> </tt>
<a name="L1249"></a><tt class="py-lineno">1249</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb.tell(B &gt;&gt; C)</tt> </tt>
<a name="L1250"></a><tt class="py-lineno">1250</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb.ask(C) ## The result {} means true, with no substitutions</tt> </tt>
<a name="L1251"></a><tt class="py-lineno">1251</tt>  <tt class="py-line"><tt class="py-string">{}</tt> </tt>
<a name="L1252"></a><tt class="py-lineno">1252</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb.ask(P) </tt> </tt>
<a name="L1253"></a><tt class="py-lineno">1253</tt>  <tt class="py-line"><tt class="py-string">False</tt> </tt>
<a name="L1254"></a><tt class="py-lineno">1254</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb.retract(B)</tt> </tt>
<a name="L1255"></a><tt class="py-lineno">1255</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; kb.ask(C) </tt> </tt>
<a name="L1256"></a><tt class="py-lineno">1256</tt>  <tt class="py-line"><tt class="py-string">False</tt> </tt>
<a name="L1257"></a><tt class="py-lineno">1257</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1258"></a><tt class="py-lineno">1258</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; pl_true(P, {}) </tt> </tt>
<a name="L1259"></a><tt class="py-lineno">1259</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; pl_true(P | Q, {P: True}) </tt> </tt>
<a name="L1260"></a><tt class="py-lineno">1260</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1261"></a><tt class="py-lineno">1261</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1262"></a><tt class="py-lineno">1262</tt>  <tt class="py-line"><tt class="py-string"># Notice that the function pl_true cannot reason by cases:</tt> </tt>
<a name="L1263"></a><tt class="py-lineno">1263</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; pl_true(P | ~P) </tt> </tt>
<a name="L1264"></a><tt class="py-lineno">1264</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1265"></a><tt class="py-lineno">1265</tt>  <tt class="py-line"><tt class="py-string"># However, tt_true can:</tt> </tt>
<a name="L1266"></a><tt class="py-lineno">1266</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true(P | ~P) </tt> </tt>
<a name="L1267"></a><tt class="py-lineno">1267</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1268"></a><tt class="py-lineno">1268</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1269"></a><tt class="py-lineno">1269</tt>  <tt class="py-line"><tt class="py-string"># The following are tautologies from [Fig. 7.11]:</tt> </tt>
<a name="L1270"></a><tt class="py-lineno">1270</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A &amp; B) &lt;=&gt; (B &amp; A)") </tt> </tt>
<a name="L1271"></a><tt class="py-lineno">1271</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1272"></a><tt class="py-lineno">1272</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A | B) &lt;=&gt; (B | A)") </tt> </tt>
<a name="L1273"></a><tt class="py-lineno">1273</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1274"></a><tt class="py-lineno">1274</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("((A &amp; B) &amp; C) &lt;=&gt; (A &amp; (B &amp; C))") </tt> </tt>
<a name="L1275"></a><tt class="py-lineno">1275</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1276"></a><tt class="py-lineno">1276</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("((A | B) | C) &lt;=&gt; (A | (B | C))") </tt> </tt>
<a name="L1277"></a><tt class="py-lineno">1277</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1278"></a><tt class="py-lineno">1278</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("~~A &lt;=&gt; A") </tt> </tt>
<a name="L1279"></a><tt class="py-lineno">1279</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1280"></a><tt class="py-lineno">1280</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A &gt;&gt; B) &lt;=&gt; (~B &gt;&gt; ~A)") </tt> </tt>
<a name="L1281"></a><tt class="py-lineno">1281</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1282"></a><tt class="py-lineno">1282</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A &gt;&gt; B) &lt;=&gt; (~A | B)") </tt> </tt>
<a name="L1283"></a><tt class="py-lineno">1283</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1284"></a><tt class="py-lineno">1284</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A &lt;=&gt; B) &lt;=&gt; ((A &gt;&gt; B) &amp; (B &gt;&gt; A))") </tt> </tt>
<a name="L1285"></a><tt class="py-lineno">1285</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1286"></a><tt class="py-lineno">1286</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("~(A &amp; B) &lt;=&gt; (~A | ~B)") </tt> </tt>
<a name="L1287"></a><tt class="py-lineno">1287</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1288"></a><tt class="py-lineno">1288</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("~(A | B) &lt;=&gt; (~A &amp; ~B)") </tt> </tt>
<a name="L1289"></a><tt class="py-lineno">1289</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1290"></a><tt class="py-lineno">1290</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A &amp; (B | C)) &lt;=&gt; ((A &amp; B) | (A &amp; C))") </tt> </tt>
<a name="L1291"></a><tt class="py-lineno">1291</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1292"></a><tt class="py-lineno">1292</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true("(A | (B &amp; C)) &lt;=&gt; ((A | B) &amp; (A | C))") </tt> </tt>
<a name="L1293"></a><tt class="py-lineno">1293</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1294"></a><tt class="py-lineno">1294</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1295"></a><tt class="py-lineno">1295</tt>  <tt class="py-line"><tt class="py-string"># The following are not tautologies:</tt> </tt>
<a name="L1296"></a><tt class="py-lineno">1296</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true(A &amp; ~A) </tt> </tt>
<a name="L1297"></a><tt class="py-lineno">1297</tt>  <tt class="py-line"><tt class="py-string">False</tt> </tt>
<a name="L1298"></a><tt class="py-lineno">1298</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_true(A &amp; B) </tt> </tt>
<a name="L1299"></a><tt class="py-lineno">1299</tt>  <tt class="py-line"><tt class="py-string">False</tt> </tt>
<a name="L1300"></a><tt class="py-lineno">1300</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1301"></a><tt class="py-lineno">1301</tt>  <tt class="py-line"><tt class="py-string">### [Fig. 7.13]</tt> </tt>
<a name="L1302"></a><tt class="py-lineno">1302</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; alpha = expr("~P12")</tt> </tt>
<a name="L1303"></a><tt class="py-lineno">1303</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; to_cnf(Fig[7,13] &amp; ~alpha)</tt> </tt>
<a name="L1304"></a><tt class="py-lineno">1304</tt>  <tt class="py-line"><tt class="py-string">((~P12 | B11) &amp; (~P21 | B11) &amp; (P12 | P21 | ~B11) &amp; ~B11 &amp; P12)</tt> </tt>
<a name="L1305"></a><tt class="py-lineno">1305</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; tt_entails(Fig[7,13], alpha) </tt> </tt>
<a name="L1306"></a><tt class="py-lineno">1306</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1307"></a><tt class="py-lineno">1307</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; pl_resolution(PropKB(Fig[7,13]), alpha) </tt> </tt>
<a name="L1308"></a><tt class="py-lineno">1308</tt>  <tt class="py-line"><tt class="py-string">True</tt> </tt>
<a name="L1309"></a><tt class="py-lineno">1309</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1310"></a><tt class="py-lineno">1310</tt>  <tt class="py-line"><tt class="py-string">### [Fig. 7.15]</tt> </tt>
<a name="L1311"></a><tt class="py-lineno">1311</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; pl_fc_entails(Fig[7,15], expr('SomethingSilly')) </tt> </tt>
<a name="L1312"></a><tt class="py-lineno">1312</tt>  <tt class="py-line"><tt class="py-string">False</tt> </tt>
<a name="L1313"></a><tt class="py-lineno">1313</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1314"></a><tt class="py-lineno">1314</tt>  <tt class="py-line"><tt class="py-string">### Unification:</tt> </tt>
<a name="L1315"></a><tt class="py-lineno">1315</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; unify(x, x, {}) </tt> </tt>
<a name="L1316"></a><tt class="py-lineno">1316</tt>  <tt class="py-line"><tt class="py-string">{}</tt> </tt>
<a name="L1317"></a><tt class="py-lineno">1317</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; unify(x, 3, {}) </tt> </tt>
<a name="L1318"></a><tt class="py-lineno">1318</tt>  <tt class="py-line"><tt class="py-string">{x: 3}</tt> </tt>
<a name="L1319"></a><tt class="py-lineno">1319</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1320"></a><tt class="py-lineno">1320</tt>  <tt class="py-line"><tt class="py-string"></tt> </tt>
<a name="L1321"></a><tt class="py-lineno">1321</tt>  <tt class="py-line"><tt class="py-string">&gt;&gt;&gt; to_cnf((P&amp;Q) | (~P &amp; ~Q)) </tt> </tt>
<a name="L1322"></a><tt class="py-lineno">1322</tt>  <tt class="py-line"><tt class="py-string">((~P | P) &amp; (~Q | P) &amp; (~P | Q) &amp; (~Q | Q))</tt> </tt>
<a name="L1323"></a><tt class="py-lineno">1323</tt>  <tt class="py-line"><tt class="py-string">"""</tt> </tt>
</div><a name="L1324"></a><tt class="py-lineno">1324</tt>  <tt class="py-line"> </tt><script type="text/javascript">
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